TSTP Solution File: COL088-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : COL088-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 00:39:58 EDT 2022
% Result : Unsatisfiable 1.27s 1.59s
% Output : Refutation 1.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COL088-1 : TPTP v8.1.0. Released v2.7.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 13:34:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.45/1.01 ============================== Prover9 ===============================
% 0.45/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.01 Process 32034 was started by sandbox on n021.cluster.edu,
% 0.45/1.01 Tue May 31 13:35:00 2022
% 0.45/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31881_n021.cluster.edu".
% 0.45/1.01 ============================== end of head ===========================
% 0.45/1.01
% 0.45/1.01 ============================== INPUT =================================
% 0.45/1.01
% 0.45/1.01 % Reading from file /tmp/Prover9_31881_n021.cluster.edu
% 0.45/1.01
% 0.45/1.01 set(prolog_style_variables).
% 0.45/1.01 set(auto2).
% 0.45/1.01 % set(auto2) -> set(auto).
% 0.45/1.01 % set(auto) -> set(auto_inference).
% 0.45/1.01 % set(auto) -> set(auto_setup).
% 0.45/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.01 % set(auto) -> set(auto_limits).
% 0.45/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.01 % set(auto) -> set(auto_denials).
% 0.45/1.01 % set(auto) -> set(auto_process).
% 0.45/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.01 % set(auto2) -> assign(stats, some).
% 0.45/1.01 % set(auto2) -> clear(echo_input).
% 0.45/1.01 % set(auto2) -> set(quiet).
% 0.45/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.01 % set(auto2) -> clear(print_given).
% 0.45/1.01 assign(lrs_ticks,-1).
% 0.45/1.01 assign(sos_limit,10000).
% 0.45/1.01 assign(order,kbo).
% 0.45/1.01 set(lex_order_vars).
% 0.45/1.01 clear(print_given).
% 0.45/1.01
% 0.45/1.01 % formulas(sos). % not echoed (44 formulas)
% 0.45/1.01
% 0.45/1.01 ============================== end of input ==========================
% 0.45/1.01
% 0.45/1.01 % From the command line: assign(max_seconds, 300).
% 0.45/1.01
% 0.45/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.01
% 0.45/1.01 % Formulas that are not ordinary clauses:
% 0.45/1.01
% 0.45/1.01 ============================== end of process non-clausal formulas ===
% 0.45/1.01
% 0.45/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.01
% 0.45/1.01 ============================== PREDICATE ELIMINATION =================
% 0.45/1.01 1 -trans(A) | -member(pair(B,C),A) | -member(pair(C,D),A) | member(pair(B,D),A) # label(transD) # label(axiom). [assumption].
% 0.45/1.01 2 trans(rtrancl(A)) # label(trans_rtrancl) # label(axiom). [assumption].
% 0.45/1.01 Derived: -member(pair(A,B),rtrancl(C)) | -member(pair(B,D),rtrancl(C)) | member(pair(A,D),rtrancl(C)). [resolve(1,a,2,a)].
% 0.45/1.01 3 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c1(A,B,C) | ap_contractE_c2(A,B,C) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) # label(ap_contractE1) # label(axiom). [assumption].
% 0.45/1.01 4 -ap_contractE_c1(A,B,C) | member(C,comb) # label(ap_contractE2) # label(axiom). [assumption].
% 0.45/1.01 5 -ap_contractE_c1(A,B,C) | member(B,comb) # label(ap_contractE3) # label(axiom). [assumption].
% 0.45/1.01 6 -ap_contractE_c1(A,B,C) | A = comb_app(combK,C) # label(ap_contractE4) # label(axiom). [assumption].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c2(A,B,C) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(C,comb). [resolve(3,b,4,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c2(A,B,C) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(B,comb). [resolve(3,b,5,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c2(A,B,C) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C). [resolve(3,b,6,a)].
% 0.45/1.01 7 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c2(A,B,C) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(C,comb). [resolve(3,b,4,a)].
% 0.45/1.01 8 -ap_contractE_c2(A,B,C) | member(B,comb) # label(ap_contractE7) # label(axiom). [assumption].
% 0.45/1.01 9 -ap_contractE_c2(A,B,C) | member(ap_contractE_sk1p(A,B,C),comb) # label(ap_contractE5) # label(axiom). [assumption].
% 0.45/1.01 10 -ap_contractE_c2(A,B,C) | member(ap_contractE_sk1q(A,B,C),comb) # label(ap_contractE6) # label(axiom). [assumption].
% 0.45/1.01 11 -ap_contractE_c2(A,B,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) # label(ap_contractE9) # label(axiom). [assumption].
% 0.45/1.01 12 -ap_contractE_c2(A,B,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) # label(ap_contractE8) # label(axiom). [assumption].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(C,comb) | member(B,comb). [resolve(7,b,8,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(C,comb) | member(ap_contractE_sk1p(A,B,C),comb). [resolve(7,b,9,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(C,comb) | member(ap_contractE_sk1q(A,B,C),comb). [resolve(7,b,10,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(C,comb) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)). [resolve(7,b,11,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(C,comb) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)). [resolve(7,b,12,a)].
% 0.45/1.01 13 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c2(A,B,C) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(B,comb). [resolve(3,b,5,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(B,comb) | member(B,comb). [resolve(13,b,8,a)].
% 0.45/1.01 14 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c2(A,B,C) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C). [resolve(3,b,6,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | member(ap_contractE_sk1p(A,B,C),comb). [resolve(14,b,9,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | member(ap_contractE_sk1q(A,B,C),comb). [resolve(14,b,10,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)). [resolve(14,b,11,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)). [resolve(14,b,12,a)].
% 0.45/1.01 15 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(C,comb) | member(B,comb). [resolve(7,b,8,a)].
% 0.45/1.01 16 -ap_contractE_c3(A,B,C) | member(B,comb) # label(ap_contractE11) # label(axiom). [assumption].
% 0.45/1.01 17 -ap_contractE_c3(A,B,C) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) # label(ap_contractE10) # label(axiom). [assumption].
% 0.45/1.01 18 -ap_contractE_c3(A,B,C) | C = comb_app(ap_contractE_sk2q(A,B,C),B) # label(ap_contractE12) # label(axiom). [assumption].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | member(B,comb) | member(B,comb). [resolve(15,b,16,a)].
% 0.45/1.01 19 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(C,comb) | member(ap_contractE_sk1p(A,B,C),comb). [resolve(7,b,9,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | member(ap_contractE_sk1p(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(19,b,17,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | member(ap_contractE_sk1p(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(19,b,18,a)].
% 0.45/1.01 20 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(C,comb) | member(ap_contractE_sk1q(A,B,C),comb). [resolve(7,b,10,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | member(ap_contractE_sk1q(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(20,b,17,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | member(ap_contractE_sk1q(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(20,b,18,a)].
% 0.45/1.01 21 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(C,comb) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)). [resolve(7,b,11,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(21,b,17,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(21,b,18,a)].
% 0.45/1.01 22 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(C,comb) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)). [resolve(7,b,12,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(22,b,17,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(22,b,18,a)].
% 0.45/1.01 23 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | member(B,comb) | member(B,comb). [resolve(13,b,8,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(B,comb) | member(B,comb) | member(B,comb). [resolve(23,b,16,a)].
% 0.45/1.01 24 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | member(ap_contractE_sk1p(A,B,C),comb). [resolve(14,b,9,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | member(ap_contractE_sk1p(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(24,b,17,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | member(ap_contractE_sk1p(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(24,b,18,a)].
% 0.45/1.01 25 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | member(ap_contractE_sk1q(A,B,C),comb). [resolve(14,b,10,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | member(ap_contractE_sk1q(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(25,b,17,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | member(ap_contractE_sk1q(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(25,b,18,a)].
% 0.45/1.01 26 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)). [resolve(14,b,11,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(26,b,17,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(26,b,18,a)].
% 0.45/1.01 27 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c3(A,B,C) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)). [resolve(14,b,12,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(27,b,17,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(27,b,18,a)].
% 0.45/1.01 28 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | member(B,comb) | member(B,comb). [resolve(15,b,16,a)].
% 0.45/1.01 29 -ap_contractE_c4(A,B,C) | member(A,comb) # label(ap_contractE14) # label(axiom). [assumption].
% 0.45/1.01 30 -ap_contractE_c4(A,B,C) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract) # label(ap_contractE13) # label(axiom). [assumption].
% 0.45/1.01 31 -ap_contractE_c4(A,B,C) | C = comb_app(A,ap_contractE_sk3q(A,B,C)) # label(ap_contractE15) # label(axiom). [assumption].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(B,comb) | member(B,comb) | member(A,comb). [resolve(28,b,29,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(B,comb) | member(B,comb) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(28,b,30,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(B,comb) | member(B,comb) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(28,b,31,a)].
% 0.45/1.01 32 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | member(ap_contractE_sk1p(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(19,b,17,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(ap_contractE_sk1p(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(A,comb). [resolve(32,b,29,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(ap_contractE_sk1p(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(32,b,30,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(ap_contractE_sk1p(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(32,b,31,a)].
% 0.45/1.01 33 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | member(ap_contractE_sk1p(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(19,b,18,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(ap_contractE_sk1p(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(A,comb). [resolve(33,b,29,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(ap_contractE_sk1p(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(33,b,30,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(ap_contractE_sk1p(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(33,b,31,a)].
% 0.45/1.01 34 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | member(ap_contractE_sk1q(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(20,b,17,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(ap_contractE_sk1q(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(A,comb). [resolve(34,b,29,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(ap_contractE_sk1q(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(34,b,30,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(ap_contractE_sk1q(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(34,b,31,a)].
% 0.45/1.01 35 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | member(ap_contractE_sk1q(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(20,b,18,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(ap_contractE_sk1q(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(A,comb). [resolve(35,b,29,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(ap_contractE_sk1q(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(35,b,30,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | member(ap_contractE_sk1q(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(35,b,31,a)].
% 0.45/1.01 36 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(21,b,17,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(A,comb). [resolve(36,b,29,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(36,b,30,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(36,b,31,a)].
% 0.45/1.01 37 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(21,b,18,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(A,comb). [resolve(37,b,29,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(37,b,30,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(37,b,31,a)].
% 0.45/1.01 38 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(22,b,17,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(A,comb). [resolve(38,b,29,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(38,b,30,a)].
% 0.45/1.01 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(38,b,31,a)].
% 0.45/1.01 39 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(C,comb) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(22,b,18,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(A,comb). [resolve(39,b,29,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(39,b,30,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | member(C,comb) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(39,b,31,a)].
% 0.45/1.02 40 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | member(B,comb) | member(B,comb) | member(B,comb). [resolve(23,b,16,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | member(B,comb) | member(B,comb) | member(B,comb) | member(A,comb). [resolve(40,b,29,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | member(B,comb) | member(B,comb) | member(B,comb) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(40,b,30,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | member(B,comb) | member(B,comb) | member(B,comb) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(40,b,31,a)].
% 0.45/1.02 41 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | member(ap_contractE_sk1p(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(24,b,17,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | member(ap_contractE_sk1p(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(A,comb). [resolve(41,b,29,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | member(ap_contractE_sk1p(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(41,b,30,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | member(ap_contractE_sk1p(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(41,b,31,a)].
% 0.45/1.02 42 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | member(ap_contractE_sk1p(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(24,b,18,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | member(ap_contractE_sk1p(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(A,comb). [resolve(42,b,29,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | member(ap_contractE_sk1p(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(42,b,30,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | member(ap_contractE_sk1p(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(42,b,31,a)].
% 0.45/1.02 43 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | member(ap_contractE_sk1q(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(25,b,17,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | member(ap_contractE_sk1q(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(A,comb). [resolve(43,b,29,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | member(ap_contractE_sk1q(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(43,b,30,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | member(ap_contractE_sk1q(A,B,C),comb) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(43,b,31,a)].
% 0.45/1.02 44 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | member(ap_contractE_sk1q(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(25,b,18,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | member(ap_contractE_sk1q(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(A,comb). [resolve(44,b,29,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | member(ap_contractE_sk1q(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(44,b,30,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | member(ap_contractE_sk1q(A,B,C),comb) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(44,b,31,a)].
% 0.45/1.02 45 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(26,b,17,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(A,comb). [resolve(45,b,29,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(45,b,30,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(45,b,31,a)].
% 0.45/1.02 46 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(26,b,18,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(A,comb). [resolve(46,b,29,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(46,b,30,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(46,b,31,a)].
% 0.45/1.02 47 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract). [resolve(27,b,17,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(A,comb). [resolve(47,b,29,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(47,b,30,a)].
% 0.45/1.02 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | member(pair(A,ap_contractE_sk2q(A,B,C)),contract) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(47,b,31,a)].
% 1.27/1.59 48 -member(pair(comb_app(A,B),C),contract) | ap_contractE_c4(A,B,C) | A = comb_app(combK,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | C = comb_app(ap_contractE_sk2q(A,B,C),B). [resolve(27,b,18,a)].
% 1.27/1.59 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(A,comb). [resolve(48,b,29,a)].
% 1.27/1.59 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | member(pair(B,ap_contractE_sk3q(A,B,C)),contract). [resolve(48,b,30,a)].
% 1.27/1.59 Derived: -member(pair(comb_app(A,B),C),contract) | A = comb_app(combK,C) | C = comb_app(comb_app(ap_contractE_sk1p(A,B,C),B),comb_app(ap_contractE_sk1q(A,B,C),B)) | C = comb_app(ap_contractE_sk2q(A,B,C),B) | C = comb_app(A,ap_contractE_sk3q(A,B,C)). [resolve(48,b,31,a)].
% 1.27/1.59
% 1.27/1.59 ============================== end predicate elimination =============
% 1.27/1.59
% 1.27/1.59 Auto_denials: (non-Horn, no changes).
% 1.27/1.59
% 1.27/1.59 Term ordering decisions:
% 1.27/1.59
% 1.27/1.59 % Assigning unary symbol rtrancl kb_weight 0 and highest precedence (17).
% 1.27/1.59 Function symbol KB weights: contract=1. comb=1. combK=1. combS=1. p=1. r=1. y=1. z=1. comb_app=1. pair=1. ap_contractE_sk2q=1. ap_contractE_sk1p=1. ap_contractE_sk1q=1. ap_contractE_sk3q=1. rtrancl=0.
% 1.27/1.59
% 1.27/1.59 ============================== end of process initial clauses ========
% 1.27/1.59
% 1.27/1.59 ============================== CLAUSES FOR SEARCH ====================
% 1.27/1.59
% 1.27/1.59 ============================== end of clauses for search =============
% 1.27/1.59
% 1.27/1.59 ============================== SEARCH ================================
% 1.27/1.59
% 1.27/1.59 % Starting search at 0.02 seconds.
% 1.27/1.59
% 1.27/1.59 ============================== PROOF =================================
% 1.27/1.59 % SZS status Unsatisfiable
% 1.27/1.59 % SZS output start Refutation
% 1.27/1.59
% 1.27/1.59 % Proof 1 at 0.58 (+ 0.01) seconds.
% 1.27/1.59 % Length of proof is 17.
% 1.27/1.59 % Level of proof is 5.
% 1.27/1.59 % Maximum clause weight is 24.000.
% 1.27/1.59 % Given clauses 141.
% 1.27/1.59
% 1.27/1.59 1 -trans(A) | -member(pair(B,C),A) | -member(pair(C,D),A) | member(pair(B,D),A) # label(transD) # label(axiom). [assumption].
% 1.27/1.59 2 trans(rtrancl(A)) # label(trans_rtrancl) # label(axiom). [assumption].
% 1.27/1.59 51 member(r,comb) # label(ap_reduce1_2h1) # label(hypothesis). [assumption].
% 1.27/1.59 53 member(pair(y,z),contract) # label(ap_reduce1_2h4) # label(hypothesis). [assumption].
% 1.27/1.59 55 member(pair(comb_app(p,r),comb_app(y,r)),rtrancl(contract)) # label(ap_reduce1_2h5) # label(hypothesis). [assumption].
% 1.27/1.59 64 -member(pair(comb_app(p,r),comb_app(z,r)),rtrancl(contract)) # label(ap_reduce1_2c1) # label(negated_conjecture). [assumption].
% 1.27/1.59 67 -member(pair(A,B),contract) | member(B,comb) # label(contract_combD2) # label(axiom). [assumption].
% 1.27/1.59 68 -member(A,comb) | member(pair(A,A),rtrancl(contract)) # label(reduction_refl) # label(axiom). [assumption].
% 1.27/1.59 71 -member(A,comb) | -member(B,comb) | member(comb_app(A,B),comb) # label(comb_intros3) # label(axiom). [assumption].
% 1.27/1.59 75 -member(pair(A,B),contract) | -member(C,comb) | -member(pair(comb_app(B,C),D),rtrancl(contract)) | member(pair(comb_app(A,C),D),rtrancl(contract)) # label(reduction_rls_3) # label(axiom). [assumption].
% 1.27/1.59 79 -member(pair(A,B),rtrancl(C)) | -member(pair(B,D),rtrancl(C)) | member(pair(A,D),rtrancl(C)). [resolve(1,a,2,a)].
% 1.27/1.59 170 member(z,comb). [resolve(67,a,53,a)].
% 1.27/1.59 186 -member(A,comb) | member(comb_app(A,r),comb). [resolve(71,b,51,a)].
% 1.27/1.59 238 -member(pair(comb_app(y,r),comb_app(z,r)),rtrancl(contract)). [ur(79,a,55,a,c,64,a)].
% 1.27/1.59 1413 -member(pair(comb_app(z,r),comb_app(z,r)),rtrancl(contract)). [ur(75,a,53,a,b,51,a,d,238,a)].
% 1.27/1.59 1414 -member(comb_app(z,r),comb). [ur(68,b,1413,a)].
% 1.27/1.59 1534 $F. [resolve(186,a,170,a),unit_del(a,1414)].
% 1.27/1.59
% 1.27/1.59 % SZS output end Refutation
% 1.27/1.59 ============================== end of proof ==========================
% 1.27/1.59
% 1.27/1.59 ============================== STATISTICS ============================
% 1.27/1.59
% 1.27/1.59 Given=141. Generated=6108. Kept=1432. proofs=1.
% 1.27/1.59 Usable=141. Sos=1095. Demods=0. Limbo=27, Disabled=299. Hints=0.
% 1.27/1.59 Megabytes=1.47.
% 1.27/1.59 User_CPU=0.58, System_CPU=0.01, Wall_clock=1.
% 1.27/1.59
% 1.27/1.59 ============================== end of statistics =====================
% 1.27/1.59
% 1.27/1.59 ============================== end of search =========================
% 1.27/1.59
% 1.27/1.59 THEOREM PROVED
% 1.27/1.59 % SZS status Unsatisfiable
% 1.27/1.59
% 1.27/1.59 Exiting with 1 proof.
% 1.27/1.59
% 1.27/1.59 Process 32034 exit (max_proofs) Tue May 31 13:35:01 2022
% 1.27/1.59 Prover9 interrupted
%------------------------------------------------------------------------------