%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 11:49:03 AM UTC 2026
% Result : Unsatisfiable 0.32s 0.66s
% Output : Proof 0.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n001.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 27 15:28:30 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.32/0.66 Command-line arguments: --no-flatten-goal
% 0.32/0.66
% 0.32/0.66 % SZS status Unsatisfiable
% 0.32/0.66
% 0.32/0.67 % SZS output start Proof
% 0.32/0.67 Axiom 1 (wajsberg_1): implies(truth, X) = X.
% 0.32/0.67 Axiom 2 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.32/0.67 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.32/0.67 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.32/0.67 Axiom 5 (big_V_definition): big_V(X, Y) = implies(implies(X, Y), Y).
% 0.32/0.67 Axiom 6 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 0.32/0.67 Axiom 7 (partial_order_definition2): ifeq3(implies(X, Y), truth, ordered(X, Y), true) = true.
% 0.32/0.67 Axiom 8 (partial_order_definition1): ifeq2(ordered(X, Y), true, implies(X, Y), truth) = truth.
% 0.32/0.67 Axiom 9 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 0.32/0.67 Axiom 10 (lemma_1): ifeq(ordered(X, Y), true, ordered(implies(X, Z), implies(Y, Z)), true) = true.
% 0.32/0.67
% 0.32/0.67 Lemma 11: implies(X, big_V(X, Y)) = truth.
% 0.32/0.67 Proof:
% 0.32/0.67 implies(X, big_V(X, Y))
% 0.32/0.67 = { by axiom 5 (big_V_definition) }
% 0.32/0.67 implies(X, implies(implies(X, Y), Y))
% 0.32/0.67 = { by axiom 1 (wajsberg_1) R->L }
% 0.32/0.67 implies(X, implies(implies(X, Y), implies(truth, Y)))
% 0.32/0.67 = { by axiom 1 (wajsberg_1) R->L }
% 0.32/0.67 implies(implies(truth, X), implies(implies(X, Y), implies(truth, Y)))
% 0.32/0.67 = { by axiom 9 (wajsberg_2) }
% 0.32/0.67 truth
% 0.32/0.67
% 0.32/0.67 Goal 1 (prove_mv_4): big_V(implies(x, y), implies(y, x)) = truth.
% 0.32/0.67 Proof:
% 0.32/0.67 big_V(implies(x, y), implies(y, x))
% 0.32/0.67 = { by axiom 5 (big_V_definition) }
% 0.32/0.67 implies(implies(implies(x, y), implies(y, x)), implies(y, x))
% 0.32/0.67 = { by axiom 3 (ifeq_axiom) R->L }
% 0.32/0.67 ifeq2(true, true, implies(implies(implies(x, y), implies(y, x)), implies(y, x)), truth)
% 0.32/0.67 = { by axiom 10 (lemma_1) R->L }
% 0.32/0.67 ifeq2(ifeq(ordered(implies(x, y), truth), true, ordered(implies(implies(x, y), implies(y, x)), implies(truth, implies(y, x))), true), true, implies(implies(implies(x, y), implies(y, x)), implies(y, x)), truth)
% 0.32/0.67 = { by axiom 2 (ifeq_axiom) R->L }
% 0.32/0.67 ifeq2(ifeq(ifeq3(truth, truth, ordered(implies(x, y), truth), true), true, ordered(implies(implies(x, y), implies(y, x)), implies(truth, implies(y, x))), true), true, implies(implies(implies(x, y), implies(y, x)), implies(y, x)), truth)
% 0.32/0.67 = { by lemma 11 R->L }
% 0.32/0.67 ifeq2(ifeq(ifeq3(implies(implies(x, y), big_V(implies(x, y), truth)), truth, ordered(implies(x, y), truth), true), true, ordered(implies(implies(x, y), implies(y, x)), implies(truth, implies(y, x))), true), true, implies(implies(implies(x, y), implies(y, x)), implies(y, x)), truth)
% 0.32/0.67 = { by axiom 5 (big_V_definition) }
% 0.32/0.67 ifeq2(ifeq(ifeq3(implies(implies(x, y), implies(implies(implies(x, y), truth), truth)), truth, ordered(implies(x, y), truth), true), true, ordered(implies(implies(x, y), implies(y, x)), implies(truth, implies(y, x))), true), true, implies(implies(implies(x, y), implies(y, x)), implies(y, x)), truth)
% 0.32/0.67 = { by axiom 6 (wajsberg_3) R->L }
% 0.32/0.67 ifeq2(ifeq(ifeq3(implies(implies(x, y), implies(implies(truth, implies(x, y)), implies(x, y))), truth, ordered(implies(x, y), truth), true), true, ordered(implies(implies(x, y), implies(y, x)), implies(truth, implies(y, x))), true), true, implies(implies(implies(x, y), implies(y, x)), implies(y, x)), truth)
% 0.32/0.67 = { by axiom 5 (big_V_definition) R->L }
% 0.32/0.67 ifeq2(ifeq(ifeq3(implies(implies(x, y), big_V(truth, implies(x, y))), truth, ordered(implies(x, y), truth), true), true, ordered(implies(implies(x, y), implies(y, x)), implies(truth, implies(y, x))), true), true, implies(implies(implies(x, y), implies(y, x)), implies(y, x)), truth)
% 0.32/0.67 = { by axiom 1 (wajsberg_1) R->L }
% 0.32/0.67 ifeq2(ifeq(ifeq3(implies(implies(x, y), implies(truth, big_V(truth, implies(x, y)))), truth, ordered(implies(x, y), truth), true), true, ordered(implies(implies(x, y), implies(y, x)), implies(truth, implies(y, x))), true), true, implies(implies(implies(x, y), implies(y, x)), implies(y, x)), truth)
% 0.32/0.67 = { by lemma 11 }
% 0.32/0.67 ifeq2(ifeq(ifeq3(implies(implies(x, y), truth), truth, ordered(implies(x, y), truth), true), true, ordered(implies(implies(x, y), implies(y, x)), implies(truth, implies(y, x))), true), true, implies(implies(implies(x, y), implies(y, x)), implies(y, x)), truth)
% 0.32/0.67 = { by axiom 7 (partial_order_definition2) }
% 0.32/0.67 ifeq2(ifeq(true, true, ordered(implies(implies(x, y), implies(y, x)), implies(truth, implies(y, x))), true), true, implies(implies(implies(x, y), implies(y, x)), implies(y, x)), truth)
% 0.32/0.67 = { by axiom 4 (ifeq_axiom) }
% 0.32/0.67 ifeq2(ordered(implies(implies(x, y), implies(y, x)), implies(truth, implies(y, x))), true, implies(implies(implies(x, y), implies(y, x)), implies(y, x)), truth)
% 0.32/0.67 = { by axiom 1 (wajsberg_1) }
% 0.32/0.67 ifeq2(ordered(implies(implies(x, y), implies(y, x)), implies(y, x)), true, implies(implies(implies(x, y), implies(y, x)), implies(y, x)), truth)
% 0.32/0.67 = { by axiom 8 (partial_order_definition1) }
% 0.32/0.67 truth
% 0.32/0.67 % SZS output end Proof
% 0.32/0.67
% 0.32/0.67 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------