%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO075-1 : TPTP v9.2.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 : Tue May 5 04:11:25 PM UTC 2026
% Result : Unsatisfiable 1.34s 1.96s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 3 RR)
% Number of literals : 31 ( 30 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sh_1,axiom,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(X3,X1))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sh_1) ).
cnf(prove_meredith_2_basis_1,negated_conjecture,
nand(nand(a,a),nand(b,a)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_meredith_2_basis_1) ).
cnf(c_0_2,axiom,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(X3,X1))) = X2,
sh_1 ).
cnf(c_0_3,plain,
nand(nand(nand(X1,nand(X2,X3)),nand(nand(X4,nand(X1,nand(X2,X3))),nand(X1,nand(X2,X3)))),nand(X4,X1)) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
nand(nand(nand(X1,X2),nand(nand(X3,nand(X1,X2)),nand(X1,X2))),nand(X3,X1)) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(X3,nand(nand(X1,X3),X3)))) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_2]) ).
cnf(c_0_6,plain,
nand(nand(X1,nand(nand(nand(X2,nand(nand(X2,X2),X2)),X1),X1)),X2) = nand(X2,nand(nand(X2,X2),X2)),
inference(spm,[status(thm)],[c_0_5,c_0_2]) ).
cnf(c_0_7,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(nand(X2,X2),X2))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_2]),c_0_5]),c_0_5]) ).
cnf(c_0_8,plain,
nand(X1,nand(nand(X1,X1),X1)) = nand(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_5]) ).
cnf(c_0_9,plain,
nand(nand(X1,X1),nand(X1,nand(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_8]) ).
cnf(c_0_10,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,X2)) = X2,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
nand(nand(X1,X1),nand(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_8]),c_0_8]) ).
cnf(c_0_12,plain,
nand(nand(nand(X1,nand(X2,X1)),nand(X1,nand(X1,nand(X2,X1)))),nand(nand(X1,X1),X1)) = nand(X1,X1),
inference(spm,[status(thm)],[c_0_4,c_0_9]) ).
cnf(c_0_13,plain,
nand(nand(nand(X1,nand(X2,X1)),nand(X1,nand(X1,nand(X2,X1)))),X1) = nand(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_9]),c_0_11]) ).
cnf(c_0_14,plain,
nand(nand(X1,nand(X2,X1)),nand(X1,nand(X1,nand(X2,X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_12]),c_0_13]),c_0_8]),c_0_11]) ).
cnf(c_0_15,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(X1,nand(X3,X1)))) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_14]) ).
cnf(c_0_16,plain,
nand(nand(nand(X1,nand(X2,X1)),nand(X1,nand(X2,X1))),X1) = nand(X1,nand(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_14]),c_0_8]) ).
cnf(c_0_17,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(X1,nand(X1,nand(X3,X1))))) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
nand(X1,nand(nand(X1,nand(X2,X1)),X1)) = nand(X1,nand(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_14]) ).
cnf(c_0_19,plain,
nand(nand(X1,nand(nand(nand(X1,nand(X2,X1)),X1),X1)),X1) = nand(X1,nand(X2,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_20,plain,
nand(X1,nand(nand(nand(X1,nand(X2,X1)),X1),X1)) = nand(X1,nand(X1,nand(X2,X1))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
nand(nand(X1,nand(X1,nand(X2,X1))),X1) = nand(X1,nand(X2,X1)),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
nand(X1,nand(nand(X2,nand(nand(X1,X2),X2)),nand(X3,nand(X1,X1)))) = nand(X2,nand(nand(X1,X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_10]),c_0_9]) ).
cnf(c_0_23,plain,
nand(X1,nand(X1,nand(X1,nand(X2,X1)))) = nand(X1,nand(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_21]),c_0_18]) ).
cnf(c_0_24,plain,
nand(X1,nand(nand(X2,nand(nand(X1,X2),X2)),X1)) = nand(X2,nand(nand(X1,X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_10]),c_0_9]) ).
cnf(c_0_25,plain,
nand(X1,nand(nand(X1,nand(X2,X1)),nand(X3,nand(X1,X1)))) = nand(X1,nand(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14]),c_0_21]),c_0_14]),c_0_21]) ).
cnf(c_0_26,plain,
nand(nand(X1,X1),nand(X2,nand(nand(X1,X2),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_24]),c_0_8]) ).
cnf(c_0_27,plain,
nand(X1,nand(nand(X2,X1),X1)) = nand(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_2]) ).
cnf(c_0_28,negated_conjecture,
nand(nand(a,a),nand(b,a)) != a,
prove_meredith_2_basis_1 ).
cnf(c_0_29,plain,
nand(nand(X1,X1),nand(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.21 % Problem : BOO075-1 : TPTP v9.2.1. Released v2.6.0.
% 0.02/0.21 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.11/0.45 % Computer : n008.cluster.edu
% 0.11/0.45 % Model : x86_64 x86_64
% 0.11/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.45 % Memory : 8042.1875MB
% 0.11/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.45 % CPULimit : 300
% 0.11/0.45 % WCLimit : 300
% 0.11/0.45 % DateTime : Tue May 5 10:45:58 EDT 2026
% 0.11/0.46 % CPUTime :
% 0.11/0.47 % start to proof: theBenchmark
% 1.34/1.96 % Version : CSE_E---1.7
% 1.34/1.96 % Problem : theBenchmark.p
% 1.34/1.96 % SZS status Unsatisfiable for theBenchmark.p
% 1.34/1.96 % SZS output start CNFRefutation
% See solution above
% 1.34/1.97 % Total time : 1.386s
%------------------------------------------------------------------------------