TSTP Solution File: ALG004-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG004-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 : Thu Jul 14 17:53:34 EDT 2022
% Result : Unsatisfiable 2.34s 2.68s
% Output : Refutation 2.34s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG004-1 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 19:57:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.34/2.68 ============================== Prover9 ===============================
% 2.34/2.68 Prover9 (32) version 2009-11A, November 2009.
% 2.34/2.68 Process 4397 was started by sandbox2 on n028.cluster.edu,
% 2.34/2.68 Wed Jun 8 19:57:17 2022
% 2.34/2.68 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4244_n028.cluster.edu".
% 2.34/2.68 ============================== end of head ===========================
% 2.34/2.68
% 2.34/2.68 ============================== INPUT =================================
% 2.34/2.68
% 2.34/2.68 % Reading from file /tmp/Prover9_4244_n028.cluster.edu
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% 2.34/2.68 set(prolog_style_variables).
% 2.34/2.68 set(auto2).
% 2.34/2.68 % set(auto2) -> set(auto).
% 2.34/2.68 % set(auto) -> set(auto_inference).
% 2.34/2.68 % set(auto) -> set(auto_setup).
% 2.34/2.68 % set(auto_setup) -> set(predicate_elim).
% 2.34/2.68 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.34/2.68 % set(auto) -> set(auto_limits).
% 2.34/2.68 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.34/2.68 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.34/2.68 % set(auto) -> set(auto_denials).
% 2.34/2.68 % set(auto) -> set(auto_process).
% 2.34/2.68 % set(auto2) -> assign(new_constants, 1).
% 2.34/2.68 % set(auto2) -> assign(fold_denial_max, 3).
% 2.34/2.68 % set(auto2) -> assign(max_weight, "200.000").
% 2.34/2.68 % set(auto2) -> assign(max_hours, 1).
% 2.34/2.68 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.34/2.68 % set(auto2) -> assign(max_seconds, 0).
% 2.34/2.68 % set(auto2) -> assign(max_minutes, 5).
% 2.34/2.68 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.34/2.68 % set(auto2) -> set(sort_initial_sos).
% 2.34/2.68 % set(auto2) -> assign(sos_limit, -1).
% 2.34/2.68 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.34/2.68 % set(auto2) -> assign(max_megs, 400).
% 2.34/2.68 % set(auto2) -> assign(stats, some).
% 2.34/2.68 % set(auto2) -> clear(echo_input).
% 2.34/2.68 % set(auto2) -> set(quiet).
% 2.34/2.68 % set(auto2) -> clear(print_initial_clauses).
% 2.34/2.68 % set(auto2) -> clear(print_given).
% 2.34/2.68 assign(lrs_ticks,-1).
% 2.34/2.68 assign(sos_limit,10000).
% 2.34/2.68 assign(order,kbo).
% 2.34/2.68 set(lex_order_vars).
% 2.34/2.68 clear(print_given).
% 2.34/2.68
% 2.34/2.68 % formulas(sos). % not echoed (7 formulas)
% 2.34/2.68
% 2.34/2.68 ============================== end of input ==========================
% 2.34/2.68
% 2.34/2.68 % From the command line: assign(max_seconds, 300).
% 2.34/2.68
% 2.34/2.68 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.34/2.68
% 2.34/2.68 % Formulas that are not ordinary clauses:
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% 2.34/2.68 ============================== end of process non-clausal formulas ===
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% 2.34/2.68 ============================== PROCESS INITIAL CLAUSES ===============
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% 2.34/2.68 ============================== PREDICATE ELIMINATION =================
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% 2.34/2.68 ============================== end predicate elimination =============
% 2.34/2.68
% 2.34/2.68 Auto_denials:
% 2.34/2.68 % copying label prove_quotient_condition4 to answer in negative clause
% 2.34/2.68
% 2.34/2.68 Term ordering decisions:
% 2.34/2.68 Function symbol KB weights: a=1. a0=1. b=1. b0=1. c=1. c0=1. d=1. d0=1. multiply=1.
% 2.34/2.68
% 2.34/2.68 ============================== end of process initial clauses ========
% 2.34/2.68
% 2.34/2.68 ============================== CLAUSES FOR SEARCH ====================
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% 2.34/2.68 ============================== end of clauses for search =============
% 2.34/2.68
% 2.34/2.68 ============================== SEARCH ================================
% 2.34/2.68
% 2.34/2.68 % Starting search at 0.01 seconds.
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% 2.34/2.68 ============================== PROOF =================================
% 2.34/2.68 % SZS status Unsatisfiable
% 2.34/2.68 % SZS output start Refutation
% 2.34/2.68
% 2.34/2.68 % Proof 1 at 1.71 (+ 0.01) seconds: prove_quotient_condition4.
% 2.34/2.68 % Length of proof is 21.
% 2.34/2.68 % Level of proof is 6.
% 2.34/2.68 % Maximum clause weight is 29.000.
% 2.34/2.68 % Given clauses 108.
% 2.34/2.68
% 2.34/2.68 1 multiply(b,b0) = multiply(a,a0) # label(prove_quotient_condition1) # label(negated_conjecture). [assumption].
% 2.34/2.68 2 multiply(d,b0) = multiply(c,a0) # label(prove_quotient_condition2) # label(negated_conjecture). [assumption].
% 2.34/2.68 3 multiply(b,d0) = multiply(a,c0) # label(prove_quotient_condition3) # label(negated_conjecture). [assumption].
% 2.34/2.68 4 multiply(multiply(A,B),multiply(C,D)) = multiply(multiply(A,C),multiply(B,D)) # label(medial_law) # label(axiom). [assumption].
% 2.34/2.68 5 multiply(d,d0) != multiply(c,c0) # label(prove_quotient_condition4) # label(negated_conjecture) # answer(prove_quotient_condition4). [assumption].
% 2.34/2.68 6 multiply(A,B) != C | multiply(D,B) != C | A = D # label(left_cancellation) # label(axiom). [assumption].
% 2.34/2.68 7 multiply(A,B) != C | multiply(A,D) != C | B = D # label(right_cancelaation) # label(axiom). [assumption].
% 2.34/2.68 8 multiply(d,d0) = c_0. [new_symbol(5)].
% 2.34/2.68 9 multiply(c,c0) != c_0 # answer(prove_quotient_condition4). [back_rewrite(5),rewrite([8(3)]),flip(a)].
% 2.34/2.68 10 multiply(multiply(a,a0),multiply(A,B)) = multiply(multiply(b,A),multiply(b0,B)). [para(1(a,1),4(a,1,1))].
% 2.34/2.68 12 multiply(multiply(c,a0),multiply(A,B)) = multiply(multiply(d,A),multiply(b0,B)). [para(2(a,1),4(a,1,1))].
% 2.34/2.68 27 multiply(multiply(A,d),multiply(B,d0)) = multiply(multiply(A,B),c_0). [para(8(a,1),4(a,1,2)),flip(a)].
% 2.34/2.68 30 multiply(A,multiply(c,c0)) != multiply(A,c_0) # answer(prove_quotient_condition4). [ur(7,b,xx,c,9,a)].
% 2.34/2.68 44 multiply(multiply(A,multiply(b,B)),multiply(C,multiply(b0,D))) = multiply(multiply(A,C),multiply(multiply(a,a0),multiply(B,D))). [para(10(a,2),4(a,1,2)),flip(a)].
% 2.34/2.68 51 multiply(multiply(A,B),multiply(multiply(c,c0),C)) != multiply(multiply(A,c_0),multiply(B,C)) # answer(prove_quotient_condition4). [ur(6,a,4,a,c,30,a),flip(a)].
% 2.34/2.68 137 multiply(multiply(d,A),multiply(b0,B)) = multiply(multiply(c,A),multiply(a0,B)). [para(12(a,1),4(a,1))].
% 2.34/2.68 179 multiply(multiply(A,d),multiply(a,c0)) = multiply(multiply(A,b),c_0). [para(3(a,1),27(a,1,2))].
% 2.34/2.68 245 multiply(multiply(multiply(A,B),multiply(C,D)),multiply(multiply(c,c0),E)) != multiply(multiply(multiply(A,C),c_0),multiply(multiply(B,D),E)) # answer(prove_quotient_condition4). [para(4(a,1),51(a,1,1))].
% 2.34/2.68 275 multiply(multiply(A,a),multiply(d,c0)) = multiply(multiply(A,b),c_0). [para(179(a,1),4(a,1)),flip(a)].
% 2.34/2.68 4177 multiply(multiply(multiply(A,a),multiply(b,B)),multiply(multiply(c,c0),multiply(a0,C))) = multiply(multiply(multiply(A,b),c_0),multiply(multiply(a,a0),multiply(B,C))). [para(275(a,1),44(a,2,1)),rewrite([137(11)])].
% 2.34/2.68 4178 $F # answer(prove_quotient_condition4). [resolve(4177,a,245,a)].
% 2.34/2.68
% 2.34/2.68 % SZS output end Refutation
% 2.34/2.68 ============================== end of proof ==========================
% 2.34/2.68
% 2.34/2.68 ============================== STATISTICS ============================
% 2.34/2.68
% 2.34/2.68 Given=108. Generated=20726. Kept=4177. proofs=1.
% 2.34/2.68 Usable=97. Sos=3005. Demods=80. Limbo=420, Disabled=661. Hints=0.
% 2.34/2.68 Megabytes=5.11.
% 2.34/2.68 User_CPU=1.71, System_CPU=0.01, Wall_clock=2.
% 2.34/2.68
% 2.34/2.68 ============================== end of statistics =====================
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% 2.34/2.68 ============================== end of search =========================
% 2.34/2.68
% 2.34/2.68 THEOREM PROVED
% 2.34/2.68 % SZS status Unsatisfiable
% 2.34/2.68
% 2.34/2.68 Exiting with 1 proof.
% 2.34/2.68
% 2.34/2.68 Process 4397 exit (max_proofs) Wed Jun 8 19:57:19 2022
% 2.34/2.68 Prover9 interrupted
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