%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ROB004-1 : 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 : 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 1.37s 1.76s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of clauses : 53 ( 53 unt; 0 nHn; 14 RR)
% Number of literals : 53 ( 52 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 6 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(negate_d_is_c,hypothesis,
negate(d) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',negate_d_is_c) ).
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(c_plus_d_is_d,hypothesis,
add(c,d) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_plus_d_is_d) ).
cnf(c_plus_c_is_c,hypothesis,
add(c,c) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_plus_c_is_c) ).
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_7,axiom,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
robbins_axiom ).
cnf(c_0_8,hypothesis,
negate(d) = c,
negate_d_is_c ).
cnf(c_0_9,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_10,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associativity_of_add ).
cnf(c_0_11,hypothesis,
add(c,d) = d,
c_plus_d_is_d ).
cnf(c_0_12,hypothesis,
negate(add(negate(add(X1,c)),negate(add(X1,d)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_13,hypothesis,
add(c,c) = c,
c_plus_c_is_c ).
cnf(c_0_14,hypothesis,
add(c,add(d,X1)) = add(d,X1),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,hypothesis,
negate(add(negate(add(c,X1)),negate(add(X1,d)))) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_16,hypothesis,
add(c,add(c,X1)) = add(c,X1),
inference(spm,[status(thm)],[c_0_10,c_0_13]) ).
cnf(c_0_17,hypothesis,
add(c,add(X1,d)) = add(X1,d),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_18,hypothesis,
add(c,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_10]),c_0_17]),c_0_15]) ).
cnf(c_0_19,hypothesis,
negate(add(negate(X1),negate(negate(X1)))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_18]),c_0_18]) ).
cnf(c_0_20,hypothesis,
negate(add(X1,negate(X1))) = c,
inference(spm,[status(thm)],[c_0_19,c_0_7]) ).
cnf(c_0_21,hypothesis,
add(X1,c) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_18]) ).
cnf(c_0_22,hypothesis,
negate(negate(add(X1,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_20]),c_0_21]) ).
cnf(c_0_23,hypothesis,
negate(add(X1,negate(add(X1,X1)))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_22]),c_0_9]) ).
cnf(c_0_24,hypothesis,
negate(add(c,negate(c))) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_11]),c_0_8]),c_0_8]),c_0_13]) ).
cnf(c_0_25,hypothesis,
negate(negate(add(X1,negate(negate(X1))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_20]),c_0_18]) ).
cnf(c_0_26,hypothesis,
negate(negate(add(X1,add(X1,X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_23]),c_0_21]) ).
cnf(c_0_27,hypothesis,
negate(add(negate(X1),negate(add(X1,d)))) = X1,
inference(rw,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_28,hypothesis,
negate(negate(c)) = c,
inference(rw,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_29,hypothesis,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_10]),c_0_26]) ).
cnf(c_0_30,hypothesis,
negate(negate(add(d,negate(c)))) = negate(c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_18]),c_0_9]) ).
cnf(c_0_31,plain,
add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_9]),c_0_10]) ).
cnf(c_0_32,hypothesis,
negate(negate(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_29]),c_0_29]) ).
cnf(c_0_33,hypothesis,
negate(c) = d,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_8]),c_0_30]) ).
cnf(c_0_34,hypothesis,
add(X1,add(X1,X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_29]),c_0_10]),c_0_29]) ).
cnf(c_0_35,hypothesis,
add(X1,negate(X1)) = d,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_20]),c_0_33]) ).
cnf(c_0_36,hypothesis,
add(X1,d) = d,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,hypothesis,
add(d,X1) = d,
inference(spm,[status(thm)],[c_0_9,c_0_36]) ).
cnf(c_0_38,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_39,hypothesis,
add(X1,add(negate(X1),X2)) = d,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_35]),c_0_37]) ).
cnf(c_0_40,hypothesis,
add(X1,add(X2,X1)) = add(X2,X1),
inference(spm,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_41,hypothesis,
add(X1,add(X2,negate(X1))) = d,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,hypothesis,
add(X1,negate(add(X2,negate(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_41]),c_0_8]),c_0_18]),c_0_32]) ).
cnf(c_0_43,plain,
negate(add(X1,negate(add(X1,add(negate(X2),negate(add(X1,X2))))))) = negate(add(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_7]),c_0_32]),c_0_31]),c_0_9]) ).
cnf(c_0_44,hypothesis,
add(negate(X1),negate(add(X2,X1))) = negate(X1),
inference(spm,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_45,plain,
negate(add(X1,negate(add(X1,negate(X2))))) = negate(add(X1,X2)),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,hypothesis,
add(X1,negate(add(X1,negate(X2)))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_45]),c_0_32]) ).
cnf(c_0_47,hypothesis,
add(X1,negate(add(X1,X2))) = add(X1,negate(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_46]),c_0_34]) ).
cnf(c_0_48,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
prove_huntingtons_axiom ).
cnf(c_0_49,hypothesis,
add(X1,negate(add(X2,X1))) = add(X1,negate(X2)),
inference(spm,[status(thm)],[c_0_47,c_0_9]) ).
cnf(c_0_50,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(b),negate(a)))) != b,
inference(rw,[status(thm)],[c_0_48,c_0_9]) ).
cnf(c_0_51,hypothesis,
add(negate(add(X1,X2)),negate(add(X2,negate(X1)))) = negate(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_49]),c_0_9]),c_0_44]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ROB004-1 : 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 : 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
% 1.37/1.76 % Version : CSE_E---1.7
% 1.37/1.76 % Problem : theBenchmark.p
% 1.37/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 1.37/1.76 % SZS output start CNFRefutation
% See solution above
% 1.37/1.76 % Total time : 1.368s
%------------------------------------------------------------------------------