%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : PUZ129+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:30:57 PM UTC 2026
% Result : Theorem 0.14s 0.46s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ129+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 22:45:49 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.46 Command-line arguments: --no-flatten-goal
% 0.14/0.46
% 0.14/0.46 % SZS status Theorem
% 0.14/0.46
% 0.41/0.51 % SZS output start Proof
% 0.41/0.51 Axiom 1 (prove): s = t.
% 0.41/0.51 Axiom 2 (prove_2): cyclist(t) = true.
% 0.41/0.51 Axiom 3 (prove_1): grocer(s) = true.
% 0.41/0.51 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.41/0.51 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.41/0.51 Axiom 6 (prove_14): ifeq2(cyclist(X), true, h(X), X) = X.
% 0.41/0.51 Axiom 7 (prove_16): ifeq2(cyclist(X), true, r(X), X) = X.
% 0.41/0.51 Axiom 8 (prove_17): ifeq(cyclist(X), true, person(r(X)), true) = true.
% 0.41/0.51 Axiom 9 (prove_15): ifeq(cyclist(X), true, property1(h(X), industrious, pos), true) = true.
% 0.41/0.51 Axiom 10 (prove_8): ifeq2(grocer(X), true, ifeq2(property1(X, industrious, pos), true, f(X), X), X) = X.
% 0.41/0.51 Axiom 11 (prove_9): ifeq(grocer(X), true, ifeq(property1(X, industrious, pos), true, property1(f(X), honest, pos), true), true) = true.
% 0.41/0.51 Axiom 12 (prove_3): ifeq2(property1(X, industrious, pos), true, ifeq2(property1(X, honest, pos), true, ifeq2(person(X), true, b(X), X), X), X) = X.
% 0.41/0.51 Axiom 13 (prove_4): ifeq(property1(X, industrious, pos), true, ifeq(property1(X, honest, pos), true, ifeq(person(X), true, property1(b(X), healthy, pos), true), true), true) = true.
% 0.41/0.51
% 0.41/0.51 Lemma 14: h(s) = s.
% 0.41/0.51 Proof:
% 0.41/0.51 h(s)
% 0.41/0.51 = { by axiom 5 (ifeq_axiom) R->L }
% 0.41/0.51 ifeq2(true, true, h(s), s)
% 0.41/0.51 = { by axiom 2 (prove_2) R->L }
% 0.41/0.51 ifeq2(cyclist(t), true, h(s), s)
% 0.41/0.51 = { by axiom 1 (prove) R->L }
% 0.41/0.51 ifeq2(cyclist(s), true, h(s), s)
% 0.41/0.51 = { by axiom 6 (prove_14) }
% 0.41/0.51 s
% 0.41/0.51
% 0.41/0.51 Lemma 15: f(s) = s.
% 0.41/0.51 Proof:
% 0.41/0.51 f(s)
% 0.41/0.51 = { by axiom 5 (ifeq_axiom) R->L }
% 0.41/0.51 ifeq2(true, true, f(s), s)
% 0.41/0.51 = { by axiom 5 (ifeq_axiom) R->L }
% 0.41/0.51 ifeq2(true, true, ifeq2(true, true, f(s), s), s)
% 0.41/0.51 = { by axiom 3 (prove_1) R->L }
% 0.41/0.51 ifeq2(grocer(s), true, ifeq2(true, true, f(s), s), s)
% 0.41/0.51 = { by axiom 9 (prove_15) R->L }
% 0.41/0.51 ifeq2(grocer(s), true, ifeq2(ifeq(cyclist(s), true, property1(h(s), industrious, pos), true), true, f(s), s), s)
% 0.41/0.51 = { by lemma 14 }
% 0.41/0.51 ifeq2(grocer(s), true, ifeq2(ifeq(cyclist(s), true, property1(s, industrious, pos), true), true, f(s), s), s)
% 0.41/0.51 = { by axiom 1 (prove) }
% 0.41/0.51 ifeq2(grocer(s), true, ifeq2(ifeq(cyclist(t), true, property1(s, industrious, pos), true), true, f(s), s), s)
% 0.41/0.51 = { by axiom 2 (prove_2) }
% 0.41/0.51 ifeq2(grocer(s), true, ifeq2(ifeq(true, true, property1(s, industrious, pos), true), true, f(s), s), s)
% 0.41/0.51 = { by axiom 4 (ifeq_axiom) }
% 0.41/0.51 ifeq2(grocer(s), true, ifeq2(property1(s, industrious, pos), true, f(s), s), s)
% 0.41/0.51 = { by axiom 10 (prove_8) }
% 0.41/0.51 s
% 0.41/0.51
% 0.41/0.51 Lemma 16: r(s) = s.
% 0.41/0.51 Proof:
% 0.41/0.51 r(s)
% 0.41/0.51 = { by axiom 5 (ifeq_axiom) R->L }
% 0.41/0.51 ifeq2(true, true, r(s), s)
% 0.41/0.51 = { by axiom 2 (prove_2) R->L }
% 0.41/0.51 ifeq2(cyclist(t), true, r(s), s)
% 0.41/0.51 = { by axiom 1 (prove) R->L }
% 0.41/0.51 ifeq2(cyclist(s), true, r(s), s)
% 0.41/0.51 = { by axiom 7 (prove_16) }
% 0.41/0.52 s
% 0.41/0.52
% 0.41/0.52 Goal 1 (prove_7): tuple2(property1(X, healthy, pos), grocer(X)) = tuple2(true, true).
% 0.41/0.52 The goal is true when:
% 0.41/0.52 X = s
% 0.41/0.52
% 0.41/0.52 Proof:
% 0.41/0.52 tuple2(property1(s, healthy, pos), grocer(s))
% 0.41/0.52 = { by axiom 4 (ifeq_axiom) R->L }
% 0.41/0.52 tuple2(ifeq(true, true, property1(s, healthy, pos), true), grocer(s))
% 0.41/0.52 = { by axiom 8 (prove_17) R->L }
% 0.41/0.52 tuple2(ifeq(ifeq(cyclist(s), true, person(r(s)), true), true, property1(s, healthy, pos), true), grocer(s))
% 0.41/0.52 = { by lemma 16 }
% 0.41/0.52 tuple2(ifeq(ifeq(cyclist(s), true, person(s), true), true, property1(s, healthy, pos), true), grocer(s))
% 0.41/0.52 = { by axiom 1 (prove) }
% 0.41/0.52 tuple2(ifeq(ifeq(cyclist(t), true, person(s), true), true, property1(s, healthy, pos), true), grocer(s))
% 0.41/0.52 = { by axiom 2 (prove_2) }
% 0.41/0.52 tuple2(ifeq(ifeq(true, true, person(s), true), true, property1(s, healthy, pos), true), grocer(s))
% 0.41/0.52 = { by axiom 4 (ifeq_axiom) }
% 0.41/0.52 tuple2(ifeq(person(s), true, property1(s, healthy, pos), true), grocer(s))
% 0.41/0.52 = { by axiom 4 (ifeq_axiom) R->L }
% 0.41/0.52 tuple2(ifeq(true, true, ifeq(person(s), true, property1(s, healthy, pos), true), true), grocer(s))
% 0.41/0.52 = { by axiom 11 (prove_9) R->L }
% 0.41/0.52 tuple2(ifeq(ifeq(grocer(s), true, ifeq(property1(s, industrious, pos), true, property1(f(s), honest, pos), true), true), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), grocer(s))
% 0.41/0.52 = { by lemma 15 }
% 0.41/0.52 tuple2(ifeq(ifeq(grocer(s), true, ifeq(property1(s, industrious, pos), true, property1(s, honest, pos), true), true), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), grocer(s))
% 0.41/0.52 = { by axiom 3 (prove_1) }
% 0.41/0.52 tuple2(ifeq(ifeq(true, true, ifeq(property1(s, industrious, pos), true, property1(s, honest, pos), true), true), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), grocer(s))
% 0.41/0.52 = { by axiom 4 (ifeq_axiom) }
% 0.41/0.52 tuple2(ifeq(ifeq(property1(s, industrious, pos), true, property1(s, honest, pos), true), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), grocer(s))
% 0.41/0.52 = { by axiom 4 (ifeq_axiom) R->L }
% 0.41/0.52 tuple2(ifeq(ifeq(ifeq(true, true, property1(s, industrious, pos), true), true, property1(s, honest, pos), true), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), grocer(s))
% 0.41/0.52 = { by axiom 2 (prove_2) R->L }
% 0.41/0.52 tuple2(ifeq(ifeq(ifeq(cyclist(t), true, property1(s, industrious, pos), true), true, property1(s, honest, pos), true), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), grocer(s))
% 0.41/0.52 = { by axiom 1 (prove) R->L }
% 0.41/0.52 tuple2(ifeq(ifeq(ifeq(cyclist(s), true, property1(s, industrious, pos), true), true, property1(s, honest, pos), true), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), grocer(s))
% 0.41/0.52 = { by lemma 14 R->L }
% 0.41/0.52 tuple2(ifeq(ifeq(ifeq(cyclist(s), true, property1(h(s), industrious, pos), true), true, property1(s, honest, pos), true), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), grocer(s))
% 0.41/0.52 = { by axiom 9 (prove_15) }
% 0.41/0.52 tuple2(ifeq(ifeq(true, true, property1(s, honest, pos), true), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), grocer(s))
% 0.41/0.52 = { by axiom 4 (ifeq_axiom) }
% 0.41/0.52 tuple2(ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), grocer(s))
% 0.41/0.52 = { by axiom 4 (ifeq_axiom) R->L }
% 0.41/0.52 tuple2(ifeq(true, true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 9 (prove_15) R->L }
% 0.41/0.52 tuple2(ifeq(ifeq(cyclist(s), true, property1(h(s), industrious, pos), true), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by lemma 14 }
% 0.41/0.52 tuple2(ifeq(ifeq(cyclist(s), true, property1(s, industrious, pos), true), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 1 (prove) }
% 0.41/0.52 tuple2(ifeq(ifeq(cyclist(t), true, property1(s, industrious, pos), true), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 2 (prove_2) }
% 0.41/0.52 tuple2(ifeq(ifeq(true, true, property1(s, industrious, pos), true), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 4 (ifeq_axiom) }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(s, healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 12 (prove_3) R->L }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(property1(s, industrious, pos), true, ifeq2(property1(s, honest, pos), true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 4 (ifeq_axiom) R->L }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(property1(s, industrious, pos), true, ifeq2(ifeq(true, true, property1(s, honest, pos), true), true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 9 (prove_15) R->L }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(property1(s, industrious, pos), true, ifeq2(ifeq(ifeq(cyclist(s), true, property1(h(s), industrious, pos), true), true, property1(s, honest, pos), true), true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by lemma 14 }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(property1(s, industrious, pos), true, ifeq2(ifeq(ifeq(cyclist(s), true, property1(s, industrious, pos), true), true, property1(s, honest, pos), true), true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 1 (prove) }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(property1(s, industrious, pos), true, ifeq2(ifeq(ifeq(cyclist(t), true, property1(s, industrious, pos), true), true, property1(s, honest, pos), true), true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 2 (prove_2) }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(property1(s, industrious, pos), true, ifeq2(ifeq(ifeq(true, true, property1(s, industrious, pos), true), true, property1(s, honest, pos), true), true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 4 (ifeq_axiom) }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(property1(s, industrious, pos), true, ifeq2(ifeq(property1(s, industrious, pos), true, property1(s, honest, pos), true), true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 4 (ifeq_axiom) R->L }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(property1(s, industrious, pos), true, ifeq2(ifeq(true, true, ifeq(property1(s, industrious, pos), true, property1(s, honest, pos), true), true), true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 3 (prove_1) R->L }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(property1(s, industrious, pos), true, ifeq2(ifeq(grocer(s), true, ifeq(property1(s, industrious, pos), true, property1(s, honest, pos), true), true), true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by lemma 15 R->L }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(property1(s, industrious, pos), true, ifeq2(ifeq(grocer(s), true, ifeq(property1(s, industrious, pos), true, property1(f(s), honest, pos), true), true), true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 11 (prove_9) }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(property1(s, industrious, pos), true, ifeq2(true, true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 4 (ifeq_axiom) R->L }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(ifeq(true, true, property1(s, industrious, pos), true), true, ifeq2(true, true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 2 (prove_2) R->L }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(ifeq(cyclist(t), true, property1(s, industrious, pos), true), true, ifeq2(true, true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by axiom 1 (prove) R->L }
% 0.41/0.52 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(ifeq(cyclist(s), true, property1(s, industrious, pos), true), true, ifeq2(true, true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.52 = { by lemma 14 R->L }
% 0.41/0.53 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(ifeq(cyclist(s), true, property1(h(s), industrious, pos), true), true, ifeq2(true, true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.53 = { by axiom 9 (prove_15) }
% 0.41/0.53 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(true, true, ifeq2(true, true, ifeq2(person(s), true, b(s), s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.53 = { by axiom 5 (ifeq_axiom) }
% 0.41/0.53 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(true, true, ifeq2(person(s), true, b(s), s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.53 = { by axiom 5 (ifeq_axiom) }
% 0.41/0.53 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(person(s), true, b(s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.53 = { by axiom 4 (ifeq_axiom) R->L }
% 0.41/0.53 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(ifeq(true, true, person(s), true), true, b(s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.53 = { by axiom 2 (prove_2) R->L }
% 0.41/0.53 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(ifeq(cyclist(t), true, person(s), true), true, b(s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.53 = { by axiom 1 (prove) R->L }
% 0.41/0.53 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(ifeq(cyclist(s), true, person(s), true), true, b(s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.53 = { by lemma 16 R->L }
% 0.41/0.53 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(ifeq(cyclist(s), true, person(r(s)), true), true, b(s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.53 = { by axiom 8 (prove_17) }
% 0.41/0.53 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(ifeq2(true, true, b(s), s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.53 = { by axiom 5 (ifeq_axiom) }
% 0.41/0.53 tuple2(ifeq(property1(s, industrious, pos), true, ifeq(property1(s, honest, pos), true, ifeq(person(s), true, property1(b(s), healthy, pos), true), true), true), grocer(s))
% 0.41/0.53 = { by axiom 13 (prove_4) }
% 0.41/0.53 tuple2(true, grocer(s))
% 0.41/0.53 = { by axiom 3 (prove_1) }
% 0.41/0.53 tuple2(true, true)
% 0.41/0.53 % SZS output end Proof
% 0.41/0.53
% 0.41/0.53 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------