%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT004-3 : TPTP v9.2.1. Released v1.0.0.
% 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 04:11:38 PM UTC 2026
% Result : Unsatisfiable 3.44s 3.09s
% Output : CNFRefutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 18 ( 8 unt; 0 nHn; 16 RR)
% Number of literals : 32 ( 31 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cancellation_for_product2,hypothesis,
( X1 = X3
| compose(X1,b) != X2
| compose(X3,b) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product2) ).
cnf(associativity_of_compose,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/CAT003-0.ax',associativity_of_compose) ).
cnf(h_ab_equals_g_ab,hypothesis,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_ab_equals_g_ab) ).
cnf(cancellation_for_product1,hypothesis,
( X1 = X3
| compose(X1,a) != X2
| compose(X3,a) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product1) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
cnf(c_0_5,hypothesis,
( X1 = X3
| compose(X1,b) != X2
| compose(X3,b) != X2 ),
cancellation_for_product2 ).
cnf(c_0_6,hypothesis,
( X1 = X2
| compose(X1,b) != compose(X2,b) ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_7,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
associativity_of_compose ).
cnf(c_0_8,hypothesis,
( compose(X1,X2) = X3
| compose(X1,compose(X2,b)) != compose(X3,b) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,hypothesis,
compose(h,compose(a,b)) = compose(g,compose(a,b)),
h_ab_equals_g_ab ).
cnf(c_0_10,hypothesis,
( compose(g,a) = X1
| compose(h,compose(a,b)) != compose(X1,b) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,hypothesis,
( X1 = X3
| compose(X1,a) != X2
| compose(X3,a) != X2 ),
cancellation_for_product1 ).
cnf(c_0_12,hypothesis,
( compose(g,a) = compose(X1,X2)
| compose(h,compose(a,b)) != compose(X1,compose(X2,b)) ),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_13,hypothesis,
( X1 = X2
| compose(X1,a) != compose(X2,a) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_14,hypothesis,
compose(g,a) = compose(h,a),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_15,hypothesis,
( g = X1
| compose(h,a) != compose(X1,a) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,negated_conjecture,
h != g,
prove_h_equals_g ).
cnf(c_0_17,hypothesis,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT004-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 10:46:58 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 3.44/3.09 % Version : CSE_E---1.7
% 3.44/3.09 % Problem : theBenchmark.p
% 3.44/3.09 % SZS status Unsatisfiable for theBenchmark.p
% 3.44/3.09 % SZS output start CNFRefutation
% See solution above
% 3.44/3.10 % Total time : 2.371s
%------------------------------------------------------------------------------