%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG039-1 : 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 : 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 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 55 ( 44 unt; 0 nHn; 35 RR)
% Number of literals : 70 ( 28 equ; 19 neg)
% Maximal clause size : 3 ( 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; 5 con; 0-2 aty)
% Number of variables : 52 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause44,axiom,
product(a,multiply(b,X1),multiply(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
cnf(clause35,axiom,
multiply(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(clause42,axiom,
product(d,a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
cnf(a_times_b,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(clause37,axiom,
multiply(b,a) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(clause68,axiom,
product(add(b,a),b,add(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
cnf(clause34,axiom,
add(X1,X1) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
cnf(absorbtion1,axiom,
sum(X1,add(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion1) ).
cnf(prove_c_equals_d,negated_conjecture,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(clause71,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
cnf(clause69,axiom,
product(add(b,a),a,add(d,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
cnf(c_0_15,axiom,
product(a,multiply(b,X1),multiply(X2,X1)),
clause44 ).
cnf(c_0_16,axiom,
multiply(X1,X1) = X1,
clause35 ).
cnf(c_0_17,plain,
product(a,b,multiply(X1,b)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_19,plain,
product(a,b,b),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_20,axiom,
product(d,a,d),
clause42 ).
cnf(c_0_21,plain,
( X1 = b
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
product(a,b,c),
a_times_b ).
cnf(c_0_23,plain,
( X1 = d
| ~ product(d,a,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_24,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_25,plain,
multiply(X1,b) = b,
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
( X1 = c
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_27,plain,
multiply(d,a) = d,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,axiom,
multiply(b,a) = d,
clause37 ).
cnf(c_0_29,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_30,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_31,plain,
product(X1,b,b),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,axiom,
product(add(b,a),b,add(b,c)),
clause68 ).
cnf(c_0_33,negated_conjecture,
c = b,
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_34,axiom,
add(X1,X1) = additive_identity,
clause34 ).
cnf(c_0_35,plain,
product(a,d,d),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_27]),c_0_28]) ).
cnf(c_0_36,plain,
product(a,d,multiply(X1,a)),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
cnf(c_0_37,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,axiom,
sum(X1,add(X1,X2),X2),
absorbtion1 ).
cnf(c_0_39,plain,
( X1 = b
| ~ product(X2,b,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_31]) ).
cnf(c_0_40,plain,
product(add(b,a),b,additive_identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_41,plain,
( X1 = d
| ~ product(a,d,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).
cnf(c_0_42,plain,
product(a,d,a),
inference(spm,[status(thm)],[c_0_36,c_0_16]) ).
cnf(c_0_43,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
additive_identity = b,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
c != d,
prove_c_equals_d ).
cnf(c_0_46,axiom,
product(X1,X1,X1),
clause71 ).
cnf(c_0_47,axiom,
product(add(b,a),a,add(d,a)),
clause69 ).
cnf(c_0_48,plain,
d = a,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
add(b,X1) = X1,
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
d != b,
inference(rw,[status(thm)],[c_0_45,c_0_33]) ).
cnf(c_0_51,plain,
( X1 = X2
| ~ product(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_46]) ).
cnf(c_0_52,plain,
product(a,a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_34]),c_0_49]),c_0_44]) ).
cnf(c_0_53,negated_conjecture,
b != a,
inference(rw,[status(thm)],[c_0_50,c_0_48]) ).
cnf(c_0_54,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG039-1 : 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 : n013.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 01:49:26 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------