%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ROB014-2 : 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 05:05:43 PM UTC 2026
% Result : Unsatisfiable 1.64s 1.89s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 22 unt; 0 nHn; 17 RR)
% Number of literals : 38 ( 32 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(robbins_axiom,axiom,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',robbins_axiom) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).
cnf(lemma_3_2,axiom,
( X1 = X2
| negate(add(X1,negate(add(X2,X3)))) != negate(add(X2,negate(add(X1,X3)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_2) ).
cnf(condition,hypothesis,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
cnf(associativity_of_add,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',associativity_of_add) ).
cnf(prove_base_step,negated_conjecture,
negate(add(e,multiply(one,add(d,negate(add(d,negate(e))))))) != negate(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_base_step) ).
cnf(one_times_x,axiom,
multiply(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-1.ax',one_times_x) ).
cnf(lemma_3_4,axiom,
( negate(add(X1,negate(add(X2,multiply(X4,add(X1,X3)))))) = X3
| negate(add(X1,negate(X2))) != X3
| ~ positive_integer(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_4) ).
cnf(one,axiom,
positive_integer(one),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-1.ax',one) ).
cnf(c_0_9,axiom,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
robbins_axiom ).
cnf(c_0_10,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_11,axiom,
( X1 = X2
| negate(add(X1,negate(add(X2,X3)))) != negate(add(X2,negate(add(X1,X3)))) ),
lemma_3_2 ).
cnf(c_0_12,plain,
negate(add(negate(add(X1,X2)),negate(add(negate(X2),X1)))) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,hypothesis,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
condition ).
cnf(c_0_14,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associativity_of_add ).
cnf(c_0_15,plain,
( X1 = X2
| negate(add(X1,negate(add(X2,X3)))) != negate(add(X2,negate(add(X3,X1)))) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_16,hypothesis,
negate(add(d,negate(add(e,negate(add(d,negate(e))))))) = negate(add(d,negate(e))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10]),c_0_10]) ).
cnf(c_0_17,plain,
add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_14]) ).
cnf(c_0_18,negated_conjecture,
negate(add(e,multiply(one,add(d,negate(add(d,negate(e))))))) != negate(e),
prove_base_step ).
cnf(c_0_19,axiom,
multiply(one,X1) = X1,
one_times_x ).
cnf(c_0_20,axiom,
( negate(add(X1,negate(add(X2,multiply(X4,add(X1,X3)))))) = X3
| negate(add(X1,negate(X2))) != X3
| ~ positive_integer(X4) ),
lemma_3_4 ).
cnf(c_0_21,hypothesis,
( X1 = negate(e)
| negate(add(negate(e),negate(add(negate(add(d,negate(e))),X1)))) != negate(add(X1,d)) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_22,hypothesis,
negate(add(negate(add(d,negate(e))),negate(add(e,add(d,negate(add(d,negate(e)))))))) = d,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_16]),c_0_17]),c_0_10]) ).
cnf(c_0_23,negated_conjecture,
negate(add(e,add(d,negate(add(d,negate(e)))))) != negate(e),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( negate(add(X1,negate(add(X2,multiply(X3,add(X1,negate(add(X1,negate(X2))))))))) = negate(add(X1,negate(X2)))
| ~ positive_integer(X3) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_25,axiom,
positive_integer(one),
one ).
cnf(c_0_26,hypothesis,
negate(add(d,negate(add(e,add(d,negate(add(d,negate(e)))))))) != negate(add(d,negate(e))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_10]),c_0_10]),c_0_23]) ).
cnf(c_0_27,plain,
negate(add(X1,negate(add(X2,add(X1,negate(add(X1,negate(X2)))))))) = negate(add(X1,negate(X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_19]),c_0_25])]) ).
cnf(c_0_28,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ROB014-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n013.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:56:41 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.64/1.89 % Version : CSE_E---1.7
% 1.64/1.89 % Problem : theBenchmark.p
% 1.64/1.89 % SZS status Unsatisfiable for theBenchmark.p
% 1.64/1.89 % SZS output start CNFRefutation
% See solution above
% 1.64/1.89 % Total time : 1.370s
%------------------------------------------------------------------------------