%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWX185-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:45:30 PM UTC 2026
% Result : Unsatisfiable 113.97s 14.68s
% Output : Proof 113.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX185-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n001.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 15:12:33 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 113.97/14.68 Command-line arguments: --flatten-regeneralise
% 113.97/14.68
% 113.97/14.68 % SZS status Unsatisfiable
% 113.97/14.68
% 113.97/14.69 % SZS output start Proof
% 113.97/14.69 Axiom 1 (axiom_007): assoc(eX) = eX.
% 113.97/14.69 Axiom 2 (axiom): impl(btrue, X) = X.
% 113.97/14.69 Axiom 3 (axiom_071): eq4(X, X) = btrue.
% 113.97/14.69 Axiom 4 (axiom_068): eq(X, X) = btrue.
% 113.97/14.69 Axiom 5 (axiom_009): append(nil, X) = X.
% 113.97/14.69 Axiom 6 (axiom_017): lin(eX) = cons(x, nil).
% 113.97/14.69 Axiom 7 (axiom_069): eq2(X, X) = btrue.
% 113.97/14.69 Axiom 8 (axiom_006): assoc(x2(X, Y)) = x2(assoc(X), assoc(Y)).
% 113.97/14.69 Axiom 9 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 113.97/14.69 Axiom 10 (axiom_010): append(cons(X, Y), Z) = cons(X, append(Y, Z)).
% 113.97/14.69 Axiom 11 (axiom_065): eq3(eX, x2(X, Y)) = bfalse.
% 113.97/14.69 Axiom 12 (axiom_019): prop_unambig(X, Y) = impl(eq(lin(X), lin(Y)), eq3(assoc(X), assoc(Y))).
% 113.97/14.69 Axiom 13 (axiom_016): lin(x2(X, Y)) = append(lin(X), append(cons(mul, nil), lin(Y))).
% 113.97/14.69 Axiom 14 (axiom_056): ifeq(eq3(X, Y), bfalse, eq3(x2(X, Z), x2(Y, W)), bfalse) = bfalse.
% 113.97/14.69 Axiom 15 (axiom_073): ifeq(eq2(X, Y), btrue, eq(cons(X, Z), cons(Y, W)), eq(Z, W)) = eq(Z, W).
% 113.97/14.69
% 113.97/14.69 Lemma 16: append(cons(X, nil), Y) = cons(X, Y).
% 113.97/14.69 Proof:
% 113.97/14.69 append(cons(X, nil), Y)
% 113.97/14.69 = { by axiom 10 (axiom_010) }
% 113.97/14.69 cons(X, append(nil, Y))
% 113.97/14.69 = { by axiom 5 (axiom_009) }
% 113.97/14.69 cons(X, Y)
% 113.97/14.69
% 113.97/14.69 Lemma 17: append(lin(X), cons(mul, lin(Y))) = lin(x2(X, Y)).
% 113.97/14.69 Proof:
% 113.97/14.69 append(lin(X), cons(mul, lin(Y)))
% 113.97/14.69 = { by lemma 16 R->L }
% 113.97/14.69 append(lin(X), append(cons(mul, nil), lin(Y)))
% 113.97/14.69 = { by axiom 13 (axiom_016) R->L }
% 113.97/14.69 lin(x2(X, Y))
% 113.97/14.69
% 113.97/14.69 Lemma 18: cons(x, cons(mul, lin(X))) = lin(x2(eX, X)).
% 113.97/14.69 Proof:
% 113.97/14.69 cons(x, cons(mul, lin(X)))
% 113.97/14.69 = { by lemma 16 R->L }
% 113.97/14.69 append(cons(x, nil), cons(mul, lin(X)))
% 113.97/14.69 = { by axiom 6 (axiom_017) R->L }
% 113.97/14.69 append(lin(eX), cons(mul, lin(X)))
% 113.97/14.69 = { by lemma 17 }
% 113.97/14.69 lin(x2(eX, X))
% 113.97/14.69
% 113.97/14.69 Lemma 19: eq(cons(X, Y), cons(X, Z)) = eq(Y, Z).
% 113.97/14.69 Proof:
% 113.97/14.69 eq(cons(X, Y), cons(X, Z))
% 113.97/14.69 = { by axiom 9 (ifeq_axiom) R->L }
% 113.97/14.69 ifeq(btrue, btrue, eq(cons(X, Y), cons(X, Z)), eq(Y, Z))
% 113.97/14.69 = { by axiom 7 (axiom_069) R->L }
% 113.97/14.69 ifeq(eq2(X, X), btrue, eq(cons(X, Y), cons(X, Z)), eq(Y, Z))
% 113.97/14.69 = { by axiom 15 (axiom_073) }
% 113.97/14.69 eq(Y, Z)
% 113.97/14.69
% 113.97/14.69 Goal 1 (goal): eq4(prop_unambig(X, Y), bfalse) = btrue.
% 113.97/14.69 The goal is true when:
% 113.97/14.69 X = x2(eX, x2(X, Y))
% 113.97/14.69 Y = x2(x2(eX, X), Y)
% 113.97/14.69
% 113.97/14.69 Proof:
% 113.97/14.69 eq4(prop_unambig(x2(eX, x2(X, Y)), x2(x2(eX, X), Y)), bfalse)
% 113.97/14.69 = { by axiom 12 (axiom_019) }
% 113.97/14.69 eq4(impl(eq(lin(x2(eX, x2(X, Y))), lin(x2(x2(eX, X), Y))), eq3(assoc(x2(eX, x2(X, Y))), assoc(x2(x2(eX, X), Y)))), bfalse)
% 113.97/14.69 = { by axiom 8 (axiom_006) }
% 113.97/14.69 eq4(impl(eq(lin(x2(eX, x2(X, Y))), lin(x2(x2(eX, X), Y))), eq3(x2(assoc(eX), assoc(x2(X, Y))), assoc(x2(x2(eX, X), Y)))), bfalse)
% 113.97/14.69 = { by axiom 1 (axiom_007) }
% 113.97/14.69 eq4(impl(eq(lin(x2(eX, x2(X, Y))), lin(x2(x2(eX, X), Y))), eq3(x2(eX, assoc(x2(X, Y))), assoc(x2(x2(eX, X), Y)))), bfalse)
% 113.97/14.69 = { by lemma 17 R->L }
% 113.97/14.69 eq4(impl(eq(lin(x2(eX, x2(X, Y))), append(lin(x2(eX, X)), cons(mul, lin(Y)))), eq3(x2(eX, assoc(x2(X, Y))), assoc(x2(x2(eX, X), Y)))), bfalse)
% 113.97/14.69 = { by lemma 18 R->L }
% 113.97/14.69 eq4(impl(eq(lin(x2(eX, x2(X, Y))), append(cons(x, cons(mul, lin(X))), cons(mul, lin(Y)))), eq3(x2(eX, assoc(x2(X, Y))), assoc(x2(x2(eX, X), Y)))), bfalse)
% 113.97/14.69 = { by axiom 10 (axiom_010) }
% 113.97/14.69 eq4(impl(eq(lin(x2(eX, x2(X, Y))), cons(x, append(cons(mul, lin(X)), cons(mul, lin(Y))))), eq3(x2(eX, assoc(x2(X, Y))), assoc(x2(x2(eX, X), Y)))), bfalse)
% 113.97/14.69 = { by axiom 10 (axiom_010) }
% 113.97/14.69 eq4(impl(eq(lin(x2(eX, x2(X, Y))), cons(x, cons(mul, append(lin(X), cons(mul, lin(Y)))))), eq3(x2(eX, assoc(x2(X, Y))), assoc(x2(x2(eX, X), Y)))), bfalse)
% 113.97/14.70 = { by lemma 17 }
% 113.97/14.70 eq4(impl(eq(lin(x2(eX, x2(X, Y))), cons(x, cons(mul, lin(x2(X, Y))))), eq3(x2(eX, assoc(x2(X, Y))), assoc(x2(x2(eX, X), Y)))), bfalse)
% 113.97/14.70 = { by lemma 18 R->L }
% 113.97/14.70 eq4(impl(eq(cons(x, cons(mul, lin(x2(X, Y)))), cons(x, cons(mul, lin(x2(X, Y))))), eq3(x2(eX, assoc(x2(X, Y))), assoc(x2(x2(eX, X), Y)))), bfalse)
% 113.97/14.70 = { by lemma 19 }
% 113.97/14.70 eq4(impl(eq(cons(mul, lin(x2(X, Y))), cons(mul, lin(x2(X, Y)))), eq3(x2(eX, assoc(x2(X, Y))), assoc(x2(x2(eX, X), Y)))), bfalse)
% 113.97/14.70 = { by lemma 19 }
% 113.97/14.70 eq4(impl(eq(lin(x2(X, Y)), lin(x2(X, Y))), eq3(x2(eX, assoc(x2(X, Y))), assoc(x2(x2(eX, X), Y)))), bfalse)
% 113.97/14.70 = { by axiom 8 (axiom_006) }
% 113.97/14.70 eq4(impl(eq(lin(x2(X, Y)), lin(x2(X, Y))), eq3(x2(eX, assoc(x2(X, Y))), x2(assoc(x2(eX, X)), assoc(Y)))), bfalse)
% 113.97/14.70 = { by axiom 8 (axiom_006) }
% 113.97/14.70 eq4(impl(eq(lin(x2(X, Y)), lin(x2(X, Y))), eq3(x2(eX, assoc(x2(X, Y))), x2(x2(assoc(eX), assoc(X)), assoc(Y)))), bfalse)
% 113.97/14.70 = { by axiom 9 (ifeq_axiom) R->L }
% 113.97/14.70 eq4(impl(eq(lin(x2(X, Y)), lin(x2(X, Y))), ifeq(bfalse, bfalse, eq3(x2(eX, assoc(x2(X, Y))), x2(x2(assoc(eX), assoc(X)), assoc(Y))), bfalse)), bfalse)
% 113.97/14.70 = { by axiom 11 (axiom_065) R->L }
% 113.97/14.70 eq4(impl(eq(lin(x2(X, Y)), lin(x2(X, Y))), ifeq(eq3(eX, x2(assoc(eX), assoc(X))), bfalse, eq3(x2(eX, assoc(x2(X, Y))), x2(x2(assoc(eX), assoc(X)), assoc(Y))), bfalse)), bfalse)
% 113.97/14.70 = { by axiom 14 (axiom_056) }
% 113.97/14.70 eq4(impl(eq(lin(x2(X, Y)), lin(x2(X, Y))), bfalse), bfalse)
% 113.97/14.70 = { by axiom 4 (axiom_068) }
% 113.97/14.70 eq4(impl(btrue, bfalse), bfalse)
% 113.97/14.70 = { by axiom 2 (axiom) }
% 113.97/14.70 eq4(bfalse, bfalse)
% 113.97/14.70 = { by axiom 3 (axiom_071) }
% 113.97/14.70 btrue
% 113.97/14.70 % SZS output end Proof
% 113.97/14.70
% 113.97/14.70 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------