TSTP Solution File: SYN212-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN212-1 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n011.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 : 300s
% DateTime : Fri Sep 1 03:33:37 EDT 2023
% Result : Unsatisfiable 29.23s 4.11s
% Output : Proof 29.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN212-1 : TPTP v8.1.2. Released v1.1.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 21:00:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 29.23/4.11 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 29.23/4.11
% 29.23/4.11 % SZS status Unsatisfiable
% 29.23/4.11
% 29.23/4.12 % SZS output start Proof
% 29.23/4.12 Take the following subset of the input axioms:
% 29.23/4.12 fof(axiom_13, axiom, r0(e)).
% 29.23/4.12 fof(axiom_28, axiom, k0(e)).
% 29.23/4.12 fof(axiom_30, axiom, n0(e, e)).
% 29.23/4.12 fof(prove_this, negated_conjecture, ~s4(e)).
% 29.23/4.12 fof(rule_002, axiom, ![G, H]: (l1(G, G) | ~n0(H, G))).
% 29.23/4.12 fof(rule_090, axiom, p1(e, e, e) | (~r0(e) | ~k0(e))).
% 29.23/4.12 fof(rule_137, axiom, ![C, B, A2]: (n2(A2) | ~p1(B, C, A2))).
% 29.23/4.12 fof(rule_244, axiom, ![H2]: (p3(H2, H2, H2) | ~n2(H2))).
% 29.23/4.12 fof(rule_299, axiom, ![D, C2, B2, A2_2]: (s4(A2_2) | (~p3(B2, C2, D) | ~l1(A2_2, C2)))).
% 29.23/4.12
% 29.23/4.12 Now clausify the problem and encode Horn clauses using encoding 3 of
% 29.23/4.12 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 29.23/4.12 We repeatedly replace C & s=t => u=v by the two clauses:
% 29.23/4.12 fresh(y, y, x1...xn) = u
% 29.23/4.12 C => fresh(s, t, x1...xn) = v
% 29.23/4.12 where fresh is a fresh function symbol and x1..xn are the free
% 29.23/4.12 variables of u and v.
% 29.23/4.12 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 29.23/4.12 input problem has no model of domain size 1).
% 29.23/4.12
% 29.23/4.12 The encoding turns the above axioms into the following unit equations and goals:
% 29.23/4.12
% 29.23/4.12 Axiom 1 (axiom_13): r0(e) = true.
% 29.23/4.12 Axiom 2 (axiom_30): n0(e, e) = true.
% 29.23/4.12 Axiom 3 (axiom_28): k0(e) = true.
% 29.23/4.12 Axiom 4 (rule_090): fresh320(X, X) = true.
% 29.23/4.12 Axiom 5 (rule_090): fresh321(X, X) = p1(e, e, e).
% 29.23/4.12 Axiom 6 (rule_002): fresh441(X, X, Y) = true.
% 29.23/4.12 Axiom 7 (rule_090): fresh321(k0(e), true) = fresh320(r0(e), true).
% 29.23/4.12 Axiom 8 (rule_137): fresh262(X, X, Y) = true.
% 29.23/4.12 Axiom 9 (rule_244): fresh121(X, X, Y) = true.
% 29.23/4.12 Axiom 10 (rule_299): fresh45(X, X, Y) = true.
% 29.23/4.12 Axiom 11 (rule_002): fresh441(n0(X, Y), true, Y) = l1(Y, Y).
% 29.23/4.12 Axiom 12 (rule_244): fresh121(n2(X), true, X) = p3(X, X, X).
% 29.23/4.12 Axiom 13 (rule_299): fresh46(X, X, Y, Z) = s4(Y).
% 29.23/4.12 Axiom 14 (rule_137): fresh262(p1(X, Y, Z), true, Z) = n2(Z).
% 29.23/4.12 Axiom 15 (rule_299): fresh46(p3(X, Y, Z), true, W, Y) = fresh45(l1(W, Y), true, W).
% 29.23/4.12
% 29.23/4.12 Goal 1 (prove_this): s4(e) = true.
% 29.23/4.12 Proof:
% 29.23/4.12 s4(e)
% 29.23/4.12 = { by axiom 13 (rule_299) R->L }
% 29.23/4.12 fresh46(true, true, e, e)
% 29.23/4.12 = { by axiom 9 (rule_244) R->L }
% 29.23/4.12 fresh46(fresh121(true, true, e), true, e, e)
% 29.23/4.12 = { by axiom 8 (rule_137) R->L }
% 29.23/4.12 fresh46(fresh121(fresh262(true, true, e), true, e), true, e, e)
% 29.23/4.12 = { by axiom 4 (rule_090) R->L }
% 29.23/4.12 fresh46(fresh121(fresh262(fresh320(true, true), true, e), true, e), true, e, e)
% 29.23/4.12 = { by axiom 1 (axiom_13) R->L }
% 29.23/4.12 fresh46(fresh121(fresh262(fresh320(r0(e), true), true, e), true, e), true, e, e)
% 29.23/4.12 = { by axiom 7 (rule_090) R->L }
% 29.23/4.12 fresh46(fresh121(fresh262(fresh321(k0(e), true), true, e), true, e), true, e, e)
% 29.23/4.12 = { by axiom 3 (axiom_28) }
% 29.23/4.12 fresh46(fresh121(fresh262(fresh321(true, true), true, e), true, e), true, e, e)
% 29.23/4.12 = { by axiom 5 (rule_090) }
% 29.23/4.12 fresh46(fresh121(fresh262(p1(e, e, e), true, e), true, e), true, e, e)
% 29.23/4.12 = { by axiom 14 (rule_137) }
% 29.23/4.12 fresh46(fresh121(n2(e), true, e), true, e, e)
% 29.23/4.12 = { by axiom 12 (rule_244) }
% 29.23/4.12 fresh46(p3(e, e, e), true, e, e)
% 29.23/4.12 = { by axiom 15 (rule_299) }
% 29.23/4.12 fresh45(l1(e, e), true, e)
% 29.23/4.12 = { by axiom 11 (rule_002) R->L }
% 29.23/4.12 fresh45(fresh441(n0(e, e), true, e), true, e)
% 29.23/4.12 = { by axiom 2 (axiom_30) }
% 29.23/4.12 fresh45(fresh441(true, true, e), true, e)
% 29.23/4.12 = { by axiom 6 (rule_002) }
% 29.23/4.12 fresh45(true, true, e)
% 29.23/4.12 = { by axiom 10 (rule_299) }
% 29.23/4.12 true
% 29.23/4.12 % SZS output end Proof
% 29.23/4.12
% 29.23/4.12 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------