%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HWC001-1 : TPTP v9.3.1. Bugfixed v1.1.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 10:19:21 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWC001-1 : TPTP v9.3.1. Bugfixed v1.1.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:54:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.11/0.45
% 0.11/0.45 % SZS status Unsatisfiable
% 0.11/0.45
% 0.11/0.46 % SZS output start Proof
% 0.11/0.46 Axiom 1 (not_definition2): not(n1) = n0.
% 0.11/0.46 Axiom 2 (not_definition1): not(n0) = n1.
% 0.11/0.46 Axiom 3 (and_definition2): and(X, n1) = X.
% 0.11/0.46 Axiom 4 (and_definition1): and(X, n0) = n0.
% 0.11/0.46 Axiom 5 (nand_definition): nand(X, Y) = not(and(X, Y)).
% 0.11/0.46 Axiom 6 (input2): output(n0, n1, n0, n1) = true.
% 0.11/0.46 Axiom 7 (input1): output(n0, n0, n1, n1) = true.
% 0.11/0.46 Axiom 8 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.11/0.46 Axiom 9 (nand_table_definition): ifeq(output(X, Y, Z, W), true, ifeq(output(V, U, T, S), true, output(nand(V, X), nand(U, Y), nand(T, Z), nand(S, W)), true), true) = true.
% 0.11/0.46
% 0.11/0.46 Lemma 10: nand(X, n0) = n1.
% 0.11/0.46 Proof:
% 0.11/0.46 nand(X, n0)
% 0.11/0.46 = { by axiom 5 (nand_definition) }
% 0.11/0.46 not(and(X, n0))
% 0.11/0.46 = { by axiom 4 (and_definition1) }
% 0.11/0.46 not(n0)
% 0.11/0.46 = { by axiom 2 (not_definition1) }
% 0.11/0.46 n1
% 0.11/0.46
% 0.11/0.46 Lemma 11: nand(X, n1) = not(X).
% 0.11/0.46 Proof:
% 0.11/0.46 nand(X, n1)
% 0.11/0.46 = { by axiom 5 (nand_definition) }
% 0.11/0.46 not(and(X, n1))
% 0.11/0.46 = { by axiom 3 (and_definition2) }
% 0.16/0.46 not(X)
% 0.16/0.46
% 0.16/0.46 Goal 1 (prove_cannot_make_or): output(n0, n1, n1, n1) = true.
% 0.16/0.46 Proof:
% 0.16/0.46 output(n0, n1, n1, n1)
% 0.16/0.46 = { by axiom 2 (not_definition1) R->L }
% 0.16/0.46 output(n0, n1, not(n0), n1)
% 0.16/0.46 = { by axiom 1 (not_definition2) R->L }
% 0.16/0.46 output(not(n1), n1, not(n0), n1)
% 0.16/0.46 = { by axiom 8 (ifeq_axiom) R->L }
% 0.16/0.46 ifeq(true, true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 9 (nand_table_definition) R->L }
% 0.16/0.46 ifeq(ifeq(output(n1, n0, n1, n0), true, ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 1 (not_definition2) R->L }
% 0.16/0.46 ifeq(ifeq(output(n1, not(n1), n1, n0), true, ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 1 (not_definition2) R->L }
% 0.16/0.46 ifeq(ifeq(output(n1, not(n1), n1, not(n1)), true, ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 8 (ifeq_axiom) R->L }
% 0.16/0.46 ifeq(ifeq(ifeq(true, true, output(n1, not(n1), n1, not(n1)), true), true, ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 6 (input2) R->L }
% 0.16/0.46 ifeq(ifeq(ifeq(output(n0, n1, n0, n1), true, output(n1, not(n1), n1, not(n1)), true), true, ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by lemma 11 R->L }
% 0.16/0.46 ifeq(ifeq(ifeq(output(n0, n1, n0, n1), true, output(n1, not(n1), n1, nand(n1, n1)), true), true, ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by lemma 10 R->L }
% 0.16/0.46 ifeq(ifeq(ifeq(output(n0, n1, n0, n1), true, output(n1, not(n1), nand(n0, n0), nand(n1, n1)), true), true, ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by lemma 11 R->L }
% 0.16/0.46 ifeq(ifeq(ifeq(output(n0, n1, n0, n1), true, output(n1, nand(n1, n1), nand(n0, n0), nand(n1, n1)), true), true, ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by lemma 10 R->L }
% 0.16/0.46 ifeq(ifeq(ifeq(output(n0, n1, n0, n1), true, output(nand(n0, n0), nand(n1, n1), nand(n0, n0), nand(n1, n1)), true), true, ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 8 (ifeq_axiom) R->L }
% 0.16/0.46 ifeq(ifeq(ifeq(true, true, ifeq(output(n0, n1, n0, n1), true, output(nand(n0, n0), nand(n1, n1), nand(n0, n0), nand(n1, n1)), true), true), true, ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 6 (input2) R->L }
% 0.16/0.46 ifeq(ifeq(ifeq(output(n0, n1, n0, n1), true, ifeq(output(n0, n1, n0, n1), true, output(nand(n0, n0), nand(n1, n1), nand(n0, n0), nand(n1, n1)), true), true), true, ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 9 (nand_table_definition) }
% 0.16/0.46 ifeq(ifeq(true, true, ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 8 (ifeq_axiom) }
% 0.16/0.46 ifeq(ifeq(output(n0, n0, n1, n1), true, output(nand(n0, n1), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by lemma 11 }
% 0.16/0.46 ifeq(ifeq(output(n0, n0, n1, n1), true, output(not(n0), nand(n0, n0), nand(n1, n1), nand(n1, n0)), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by lemma 10 }
% 0.16/0.46 ifeq(ifeq(output(n0, n0, n1, n1), true, output(not(n0), n1, nand(n1, n1), nand(n1, n0)), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by lemma 11 }
% 0.16/0.46 ifeq(ifeq(output(n0, n0, n1, n1), true, output(not(n0), n1, not(n1), nand(n1, n0)), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by lemma 10 }
% 0.16/0.46 ifeq(ifeq(output(n0, n0, n1, n1), true, output(not(n0), n1, not(n1), n1), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 7 (input1) }
% 0.16/0.46 ifeq(ifeq(true, true, output(not(n0), n1, not(n1), n1), true), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 8 (ifeq_axiom) }
% 0.16/0.46 ifeq(output(not(n0), n1, not(n1), n1), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 2 (not_definition1) }
% 0.16/0.46 ifeq(output(n1, n1, not(n1), n1), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by axiom 1 (not_definition2) }
% 0.16/0.46 ifeq(output(n1, n1, n0, n1), true, output(not(n1), n1, not(n0), n1), true)
% 0.16/0.46 = { by lemma 10 R->L }
% 0.16/0.46 ifeq(output(n1, n1, n0, n1), true, output(not(n1), n1, not(n0), nand(n1, n0)), true)
% 0.16/0.46 = { by lemma 11 R->L }
% 0.16/0.46 ifeq(output(n1, n1, n0, n1), true, output(not(n1), n1, nand(n0, n1), nand(n1, n0)), true)
% 0.16/0.46 = { by lemma 10 R->L }
% 0.16/0.46 ifeq(output(n1, n1, n0, n1), true, output(not(n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true)
% 0.16/0.46 = { by lemma 11 R->L }
% 0.16/0.46 ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true)
% 0.16/0.46 = { by axiom 8 (ifeq_axiom) R->L }
% 0.16/0.46 ifeq(true, true, ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true), true)
% 0.16/0.46 = { by axiom 9 (nand_table_definition) R->L }
% 0.16/0.46 ifeq(ifeq(output(n0, n1, n0, n1), true, ifeq(output(n0, n1, n0, n1), true, output(nand(n0, n0), nand(n1, n1), nand(n0, n0), nand(n1, n1)), true), true), true, ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true), true)
% 0.16/0.46 = { by axiom 6 (input2) }
% 0.16/0.46 ifeq(ifeq(true, true, ifeq(output(n0, n1, n0, n1), true, output(nand(n0, n0), nand(n1, n1), nand(n0, n0), nand(n1, n1)), true), true), true, ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true), true)
% 0.16/0.46 = { by axiom 8 (ifeq_axiom) }
% 0.16/0.46 ifeq(ifeq(output(n0, n1, n0, n1), true, output(nand(n0, n0), nand(n1, n1), nand(n0, n0), nand(n1, n1)), true), true, ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true), true)
% 0.16/0.46 = { by lemma 10 }
% 0.16/0.46 ifeq(ifeq(output(n0, n1, n0, n1), true, output(n1, nand(n1, n1), nand(n0, n0), nand(n1, n1)), true), true, ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true), true)
% 0.16/0.46 = { by lemma 11 }
% 0.16/0.46 ifeq(ifeq(output(n0, n1, n0, n1), true, output(n1, not(n1), nand(n0, n0), nand(n1, n1)), true), true, ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true), true)
% 0.16/0.46 = { by lemma 10 }
% 0.16/0.46 ifeq(ifeq(output(n0, n1, n0, n1), true, output(n1, not(n1), n1, nand(n1, n1)), true), true, ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true), true)
% 0.16/0.46 = { by lemma 11 }
% 0.16/0.46 ifeq(ifeq(output(n0, n1, n0, n1), true, output(n1, not(n1), n1, not(n1)), true), true, ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true), true)
% 0.16/0.46 = { by axiom 6 (input2) }
% 0.16/0.46 ifeq(ifeq(true, true, output(n1, not(n1), n1, not(n1)), true), true, ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true), true)
% 0.16/0.46 = { by axiom 8 (ifeq_axiom) }
% 0.16/0.46 ifeq(output(n1, not(n1), n1, not(n1)), true, ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true), true)
% 0.16/0.46 = { by axiom 1 (not_definition2) }
% 0.16/0.46 ifeq(output(n1, not(n1), n1, n0), true, ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true), true)
% 0.16/0.46 = { by axiom 1 (not_definition2) }
% 0.16/0.46 ifeq(output(n1, n0, n1, n0), true, ifeq(output(n1, n1, n0, n1), true, output(nand(n1, n1), nand(n1, n0), nand(n0, n1), nand(n1, n0)), true), true)
% 0.16/0.46 = { by axiom 9 (nand_table_definition) }
% 0.16/0.46 true
% 0.16/0.46 % SZS output end Proof
% 0.16/0.46
% 0.16/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------