%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG039-2 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n013.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 05:05:05 PM UTC 2026
% Result : Unsatisfiable 1.57s 1.82s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of clauses : 72 ( 39 unt; 0 nHn; 55 RR)
% Number of literals : 119 ( 0 equ; 51 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 107 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiplication_is_well_defined,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(clause46,axiom,
product(a,multiply(b,c),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
cnf(product_substitution3,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(clause44,axiom,
product(a,multiply(b,X1),multiply(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
cnf(multiplicative_identity1,axiom,
product(additive_identity,X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
cnf(clause71,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
cnf(product_substitution1,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).
cnf(clause41,axiom,
product(c,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
cnf(addition_is_well_defined,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(absorbtion2,axiom,
sum(add(X1,X2),X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorbtion2) ).
cnf(sum_substitution3,axiom,
( sum(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ sum(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution3) ).
cnf(clause60,axiom,
product(c,a,multiply(a,d)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
cnf(transitivity,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
cnf(clause56,axiom,
product(d,b,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
cnf(clause42,axiom,
product(d,a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
cnf(clause49,axiom,
product(b,multiply(a,d),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
cnf(product_substitution2,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).
cnf(clause50,axiom,
product(b,c,multiply(d,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
cnf(prove_c_equals_d,negated_conjecture,
~ equalish(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(c_0_20,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_21,axiom,
product(a,multiply(b,c),c),
clause46 ).
cnf(c_0_22,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3 ).
cnf(c_0_23,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_24,plain,
( equalish(X1,c)
| ~ product(a,multiply(b,c),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
product(a,multiply(b,X1),multiply(X2,X1)),
clause44 ).
cnf(c_0_26,axiom,
product(additive_identity,X1,additive_identity),
multiplicative_identity1 ).
cnf(c_0_27,plain,
( product(X1,X2,X3)
| ~ equalish(multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
equalish(multiply(X1,c),c),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,axiom,
product(X1,X1,X1),
clause71 ).
cnf(c_0_30,plain,
( equalish(X1,additive_identity)
| ~ product(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_31,plain,
product(X1,c,c),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( product(X1,X1,X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_29]) ).
cnf(c_0_33,plain,
equalish(c,additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
product_substitution1 ).
cnf(c_0_35,plain,
( equalish(X1,X2)
| ~ product(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
cnf(c_0_36,plain,
product(c,c,additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
( product(X1,X2,additive_identity)
| ~ equalish(additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_38,plain,
equalish(additive_identity,c),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
product(c,X1,additive_identity),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,axiom,
product(c,b,c),
clause41 ).
cnf(c_0_41,plain,
( product(c,X1,X2)
| ~ equalish(additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
cnf(c_0_42,plain,
( equalish(X1,c)
| ~ product(c,b,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_40]) ).
cnf(c_0_43,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_44,axiom,
sum(add(X1,X2),X2,X1),
absorbtion2 ).
cnf(c_0_45,axiom,
( sum(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ sum(X3,X4,X1) ),
sum_substitution3 ).
cnf(c_0_46,plain,
product(c,X1,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_39])]) ).
cnf(c_0_47,plain,
( equalish(X1,X2)
| ~ sum(add(X2,X3),X3,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
( sum(add(X1,X2),X2,X3)
| ~ equalish(X1,X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_49,plain,
( equalish(X1,c)
| ~ product(c,X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_46]) ).
cnf(c_0_50,axiom,
product(c,a,multiply(a,d)),
clause60 ).
cnf(c_0_51,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
transitivity ).
cnf(c_0_52,axiom,
product(d,b,multiply(b,c)),
clause56 ).
cnf(c_0_53,axiom,
product(d,a,d),
clause42 ).
cnf(c_0_54,axiom,
product(b,multiply(a,d),d),
clause49 ).
cnf(c_0_55,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
product_substitution2 ).
cnf(c_0_56,axiom,
product(b,c,multiply(d,b)),
clause50 ).
cnf(c_0_57,plain,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,plain,
equalish(multiply(a,d),c),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_59,plain,
( equalish(X1,c)
| ~ equalish(X1,multiply(X2,c)) ),
inference(spm,[status(thm)],[c_0_51,c_0_28]) ).
cnf(c_0_60,plain,
( equalish(X1,multiply(b,c))
| ~ product(d,b,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
~ equalish(c,d),
prove_c_equals_d ).
cnf(c_0_62,plain,
( equalish(X1,d)
| ~ product(d,a,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_53]) ).
cnf(c_0_63,plain,
( equalish(X1,d)
| ~ product(b,multiply(a,d),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_54]) ).
cnf(c_0_64,plain,
( product(b,X1,multiply(d,b))
| ~ equalish(c,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_65,plain,
equalish(c,multiply(a,d)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,plain,
( product(d,a,X1)
| ~ equalish(d,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_53]) ).
cnf(c_0_67,plain,
( equalish(X1,c)
| ~ product(d,b,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,negated_conjecture,
~ product(d,a,c),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_69,plain,
equalish(multiply(d,b),d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65])]) ).
cnf(c_0_70,plain,
~ product(d,b,d),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_71,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_69]),c_0_70]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG039-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.31 % Computer : n013.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue May 5 01:50:41 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.57/1.82 % Version : CSE_E---1.7
% 1.57/1.82 % Problem : theBenchmark.p
% 1.57/1.82 % SZS status Unsatisfiable for theBenchmark.p
% 1.57/1.82 % SZS output start CNFRefutation
% See solution above
% 1.57/1.82 % Total time : 1.371s
%------------------------------------------------------------------------------