%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ROB015-10 : TPTP v9.2.1. Released v7.5.0.
% 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 : n014.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 05:05:44 PM UTC 2026
% Result : Unsatisfiable 22.34s 17.51s
% Output : CNFRefutation 22.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 11 RR)
% Number of literals : 30 ( 29 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 55 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(lemma_3_2,axiom,
ifeq4(negate(add(X1,negate(add(X2,X3)))),negate(add(X2,negate(add(X1,X3)))),X1,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_2) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(lemma_3_4,axiom,
ifeq2(positive_integer(X1),true,ifeq4(negate(add(X2,negate(X3))),X4,negate(add(X2,negate(add(X3,multiply(X1,add(X2,X4)))))),X4),X4) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_4) ).
cnf(ifeq_axiom,axiom,
ifeq4(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(k_positive,axiom,
positive_integer(k) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_positive) ).
cnf(ifeq_axiom_002,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(condition,hypothesis,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
cnf(base_step,axiom,
ifeq3(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e),a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',base_step) ).
cnf(ifeq_axiom_001,axiom,
ifeq3(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(goal,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c_0_10,axiom,
ifeq4(negate(add(X1,negate(add(X2,X3)))),negate(add(X2,negate(add(X1,X3)))),X1,X2) = X2,
lemma_3_2 ).
cnf(c_0_11,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_12,axiom,
ifeq2(positive_integer(X1),true,ifeq4(negate(add(X2,negate(X3))),X4,negate(add(X2,negate(add(X3,multiply(X1,add(X2,X4)))))),X4),X4) = X4,
lemma_3_4 ).
cnf(c_0_13,axiom,
ifeq4(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_14,plain,
ifeq4(negate(add(X1,negate(add(X2,X3)))),negate(add(X2,negate(add(X3,X1)))),X1,X2) = X2,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
ifeq2(positive_integer(X1),true,negate(add(X2,negate(add(X3,multiply(X1,add(X2,negate(add(X2,negate(X3))))))))),negate(add(X2,negate(X3)))) = negate(add(X2,negate(X3))),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
positive_integer(k) = true,
k_positive ).
cnf(c_0_17,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom_002 ).
cnf(c_0_18,plain,
ifeq4(negate(add(X1,negate(add(X2,X3)))),negate(add(negate(add(X3,X1)),X2)),X1,X2) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_19,plain,
negate(add(X1,negate(add(X2,multiply(k,add(X1,negate(add(X1,negate(X2))))))))) = negate(add(X1,negate(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_20,plain,
ifeq4(negate(add(X1,negate(add(X2,X3)))),negate(add(negate(add(X2,X1)),X3)),X1,X3) = X3,
inference(spm,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_21,plain,
negate(add(X1,negate(add(X2,multiply(k,add(X1,negate(add(negate(X2),X1)))))))) = negate(add(negate(X2),X1)),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_22,hypothesis,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
condition ).
cnf(c_0_23,plain,
ifeq4(negate(add(negate(add(X1,X2)),X3)),negate(add(negate(add(X1,X3)),X2)),X3,X2) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_24,hypothesis,
negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))) = d,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_11]) ).
cnf(c_0_25,axiom,
ifeq3(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e),a,b) = b,
base_step ).
cnf(c_0_26,hypothesis,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) = negate(e),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19]),c_0_11]),c_0_22]),c_0_13]) ).
cnf(c_0_27,axiom,
ifeq3(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_28,negated_conjecture,
a != b,
goal ).
cnf(c_0_29,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.24 % Problem : ROB015-10 : TPTP v9.2.1. Released v7.5.0.
% 0.02/0.24 % 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
% 0.11/0.49 % Computer : n014.cluster.edu
% 0.11/0.49 % Model : x86_64 x86_64
% 0.11/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.49 % Memory : 8042.1875MB
% 0.11/0.49 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.49 % CPULimit : 300
% 0.11/0.49 % WCLimit : 300
% 0.11/0.49 % DateTime : Tue May 5 02:19:51 EDT 2026
% 0.11/0.49 % CPUTime :
% 0.11/0.51 % start to proof: theBenchmark
% 22.34/17.51 % Version : CSE_E---1.7
% 22.34/17.51 % Problem : theBenchmark.p
% 22.34/17.51 % SZS status Unsatisfiable for theBenchmark.p
% 22.34/17.51 % SZS output start CNFRefutation
% See solution above
% 22.34/17.59 % Total time : 13.543s
%------------------------------------------------------------------------------