%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ROB022-1 : 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 : n017.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 13.29s 8.56s
% Output : CNFRefutation 13.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 10 RR)
% Number of literals : 35 ( 34 equ; 3 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(robbins_axiom,axiom,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',robbins_axiom) ).
cnf(condition,hypothesis,
add(c,negate(c)) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).
cnf(associativity_of_add,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',associativity_of_add) ).
cnf(prove_huntingtons_axiom,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('/export/starexec/sandbox2/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,negate(c)) = c,
condition ).
cnf(c_0_7,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_8,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associativity_of_add ).
cnf(c_0_9,hypothesis,
negate(add(negate(c),negate(add(c,c)))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).
cnf(c_0_10,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
negate(add(negate(add(X1,X2)),negate(add(negate(X2),X1)))) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_12,hypothesis,
negate(add(c,negate(add(c,c)))) = negate(c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_10]),c_0_7]),c_0_6]),c_0_7]) ).
cnf(c_0_13,hypothesis,
negate(add(c,c)) = negate(c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_7]),c_0_12]),c_0_7]),c_0_6]) ).
cnf(c_0_14,plain,
negate(add(negate(add(X1,X2)),negate(add(X2,negate(X1))))) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_15,hypothesis,
add(c,add(negate(c),X1)) = add(c,X1),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_16,hypothesis,
negate(add(negate(c),negate(c))) = c,
inference(rw,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_17,plain,
negate(add(negate(add(X1,add(X2,X3))),negate(add(X2,add(X3,negate(X1)))))) = add(X2,X3),
inference(spm,[status(thm)],[c_0_14,c_0_8]) ).
cnf(c_0_18,hypothesis,
add(c,add(X1,negate(c))) = add(c,X1),
inference(spm,[status(thm)],[c_0_15,c_0_7]) ).
cnf(c_0_19,hypothesis,
negate(add(negate(add(c,X1)),negate(add(X1,add(negate(c),negate(c)))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_16]),c_0_7]) ).
cnf(c_0_20,plain,
negate(add(X1,negate(add(negate(add(X1,X2)),negate(negate(add(X1,negate(X2)))))))) = negate(add(X1,X2)),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_21,hypothesis,
add(X1,negate(c)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,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_7]) ).
cnf(c_0_23,plain,
add(X1,add(X2,X3)) = add(X3,add(X2,X1)),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_24,plain,
negate(add(X1,negate(add(negate(negate(add(X1,X2))),negate(add(X1,add(negate(add(X2,X3)),negate(add(X2,negate(X3)))))))))) = negate(add(X1,add(negate(add(X2,X3)),negate(add(X2,negate(X3)))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_5]),c_0_7]) ).
cnf(c_0_25,hypothesis,
add(negate(c),X1) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_21]) ).
cnf(c_0_26,plain,
negate(add(negate(add(X1,X2)),negate(add(negate(add(X2,X3)),add(X1,negate(add(X2,negate(X3)))))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_10]),c_0_23]) ).
cnf(c_0_27,plain,
negate(add(negate(add(negate(X1),X2)),negate(add(X1,negate(add(negate(add(negate(X1),X2)),negate(negate(add(negate(X1),negate(X2)))))))))) = negate(add(negate(add(negate(X1),X2)),negate(negate(add(negate(X1),negate(X2)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_20]),c_0_7]),c_0_7]) ).
cnf(c_0_28,hypothesis,
negate(negate(add(X1,negate(negate(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_25]),c_0_25]),c_0_5]),c_0_25]),c_0_5]),c_0_7]) ).
cnf(c_0_29,hypothesis,
negate(add(X1,negate(X1))) = negate(c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_25]),c_0_25]),c_0_5]),c_0_7]) ).
cnf(c_0_30,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
prove_huntingtons_axiom ).
cnf(c_0_31,hypothesis,
negate(negate(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_29]),c_0_25]),c_0_25]),c_0_28]),c_0_29]),c_0_25]) ).
cnf(c_0_32,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(b),negate(a)))) != b,
inference(rw,[status(thm)],[c_0_30,c_0_7]) ).
cnf(c_0_33,hypothesis,
add(negate(add(X1,X2)),negate(add(X2,negate(X1)))) = negate(X2),
inference(spm,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ROB022-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n017.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 01:51:43 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 13.29/8.56 % Version : CSE_E---1.7
% 13.29/8.56 % Problem : theBenchmark.p
% 13.29/8.56 % SZS status Unsatisfiable for theBenchmark.p
% 13.29/8.56 % SZS output start CNFRefutation
% See solution above
% 13.38/8.61 % Total time : 6.382s
%------------------------------------------------------------------------------