%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT002-1 : 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 : n001.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 04:11:37 PM UTC 2026
% Result : Unsatisfiable 1.91s 1.91s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 39 ( 19 unt; 0 nHn; 39 RR)
% Number of literals : 71 ( 9 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 56 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associative_property1,axiom,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
cnf(cg_equals_d,hypothesis,
product(c,g,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cg_equals_d) ).
cnf(associative_property2,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property2) ).
cnf(ch_equals_d,hypothesis,
product(c,h,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ch_equals_d) ).
cnf(ab_equals_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_equals_c) ).
cnf(category_theory_axiom2,axiom,
( product(X1,X6,X5)
| ~ product(X1,X2,X3)
| ~ product(X3,X4,X5)
| ~ product(X2,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom2) ).
cnf(closure_of_composition,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).
cnf(cancellation_for_product1,hypothesis,
( X1 = X3
| ~ product(a,X1,X2)
| ~ product(a,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product1) ).
cnf(cancellation_for_product2,hypothesis,
( X1 = X3
| ~ product(b,X1,X2)
| ~ product(b,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product2) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
cnf(c_0_10,axiom,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
associative_property1 ).
cnf(c_0_11,hypothesis,
product(c,g,d),
cg_equals_d ).
cnf(c_0_12,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
associative_property2 ).
cnf(c_0_13,hypothesis,
defined(c,g),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,hypothesis,
product(c,h,d),
ch_equals_d ).
cnf(c_0_15,hypothesis,
( defined(X1,g)
| ~ product(X2,X1,c) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,hypothesis,
product(a,b,c),
ab_equals_c ).
cnf(c_0_17,hypothesis,
defined(c,h),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_18,axiom,
( product(X1,X6,X5)
| ~ product(X1,X2,X3)
| ~ product(X3,X4,X5)
| ~ product(X2,X4,X6) ),
category_theory_axiom2 ).
cnf(c_0_19,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
closure_of_composition ).
cnf(c_0_20,hypothesis,
defined(b,g),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,hypothesis,
( defined(X1,h)
| ~ product(X2,X1,c) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_22,hypothesis,
( product(X1,X2,d)
| ~ product(X3,g,X2)
| ~ product(X1,X3,c) ),
inference(spm,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_23,hypothesis,
product(b,g,compose(b,g)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,hypothesis,
defined(b,h),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_25,hypothesis,
( product(X1,compose(b,g),d)
| ~ product(X1,b,c) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,hypothesis,
( product(X1,X2,d)
| ~ product(X3,h,X2)
| ~ product(X1,X3,c) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_27,hypothesis,
product(b,h,compose(b,h)),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_28,hypothesis,
( X1 = X3
| ~ product(a,X1,X2)
| ~ product(a,X3,X2) ),
cancellation_for_product1 ).
cnf(c_0_29,hypothesis,
product(a,compose(b,g),d),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_30,hypothesis,
( product(X1,compose(b,h),d)
| ~ product(X1,b,c) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,hypothesis,
( X1 = compose(b,g)
| ~ product(a,X1,d) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,hypothesis,
product(a,compose(b,h),d),
inference(spm,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_33,hypothesis,
( X1 = X3
| ~ product(b,X1,X2)
| ~ product(b,X3,X2) ),
cancellation_for_product2 ).
cnf(c_0_34,hypothesis,
compose(b,g) = compose(b,h),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,hypothesis,
( X1 = h
| ~ product(b,X1,compose(b,h)) ),
inference(spm,[status(thm)],[c_0_33,c_0_27]) ).
cnf(c_0_36,hypothesis,
product(b,g,compose(b,h)),
inference(rw,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
h != g,
prove_h_equals_g ).
cnf(c_0_38,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT002-1 : 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 : n001.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 10:47:48 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.91/1.91 % Version : CSE_E---1.7
% 1.91/1.91 % Problem : theBenchmark.p
% 1.91/1.91 % SZS status Unsatisfiable for theBenchmark.p
% 1.91/1.91 % SZS output start CNFRefutation
% See solution above
% 1.91/1.91 % Total time : 1.382s
%------------------------------------------------------------------------------