%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ROB005-1 : 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 05:05:42 PM UTC 2026
% Result : Unsatisfiable 1.66s 1.86s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 13 RR)
% Number of literals : 34 ( 33 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 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(idempotence,hypothesis,
add(c,c) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
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(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).
cnf(prove_huntingtons_axiom,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_huntingtons_axiom) ).
cnf(c_0_5,axiom,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
robbins_axiom ).
cnf(c_0_6,hypothesis,
add(c,c) = c,
idempotence ).
cnf(c_0_7,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associativity_of_add ).
cnf(c_0_8,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_9,hypothesis,
negate(add(negate(c),negate(add(c,negate(c))))) = c,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_10,plain,
add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_7]) ).
cnf(c_0_11,hypothesis,
negate(add(c,negate(add(c,add(negate(c),negate(c)))))) = negate(c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_10]),c_0_8]) ).
cnf(c_0_12,hypothesis,
add(c,add(c,X1)) = add(c,X1),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_13,plain,
negate(add(negate(add(X1,X2)),negate(add(negate(X2),X1)))) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_14,hypothesis,
negate(add(negate(c),negate(add(c,add(negate(c),negate(c)))))) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_11]),c_0_12]),c_0_8]) ).
cnf(c_0_15,plain,
negate(add(negate(add(X1,X2)),negate(add(negate(X1),X2)))) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_16,hypothesis,
negate(add(c,add(negate(c),negate(c)))) = negate(add(c,negate(c))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_8]),c_0_11]),c_0_8]) ).
cnf(c_0_17,hypothesis,
negate(add(negate(add(X1,c)),negate(add(X1,add(negate(c),negate(add(c,negate(c)))))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_8]) ).
cnf(c_0_18,hypothesis,
negate(add(negate(add(c,X1)),negate(add(c,add(negate(c),X1))))) = add(c,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_12]),c_0_10]) ).
cnf(c_0_19,hypothesis,
negate(add(c,negate(add(c,negate(c))))) = negate(c),
inference(rw,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_20,hypothesis,
negate(add(negate(c),negate(add(c,add(negate(c),negate(add(c,negate(c)))))))) = c,
inference(spm,[status(thm)],[c_0_17,c_0_6]) ).
cnf(c_0_21,hypothesis,
add(c,negate(add(c,negate(c)))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_22,plain,
negate(add(negate(add(X1,X2)),negate(add(X2,negate(X1))))) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_23,hypothesis,
add(c,add(X1,negate(add(c,negate(c))))) = add(X1,c),
inference(spm,[status(thm)],[c_0_10,c_0_21]) ).
cnf(c_0_24,hypothesis,
add(X1,negate(add(c,negate(c)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_7]),c_0_8]),c_0_17]) ).
cnf(c_0_25,plain,
negate(add(negate(add(X1,X2)),negate(add(X1,add(negate(add(X2,X3)),negate(add(X2,negate(X3)))))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_5]),c_0_8]) ).
cnf(c_0_26,hypothesis,
add(negate(add(c,negate(c))),X1) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_24]) ).
cnf(c_0_27,hypothesis,
negate(add(X1,negate(X1))) = negate(add(c,negate(c))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_26]),c_0_5]),c_0_8]) ).
cnf(c_0_28,hypothesis,
negate(negate(add(X1,negate(negate(X1))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_27]),c_0_26]) ).
cnf(c_0_29,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
prove_huntingtons_axiom ).
cnf(c_0_30,hypothesis,
negate(negate(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_27]),c_0_24]),c_0_8]),c_0_28]) ).
cnf(c_0_31,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(b),negate(a)))) != b,
inference(rw,[status(thm)],[c_0_29,c_0_8]) ).
cnf(c_0_32,hypothesis,
add(negate(add(X1,X2)),negate(add(X2,negate(X1)))) = negate(X2),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ROB005-1 : 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 01:51:41 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.66/1.86 % Version : CSE_E---1.7
% 1.66/1.86 % Problem : theBenchmark.p
% 1.66/1.86 % SZS status Unsatisfiable for theBenchmark.p
% 1.66/1.86 % SZS output start CNFRefutation
% See solution above
% 1.66/1.86 % Total time : 1.372s
%------------------------------------------------------------------------------