%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM003-1 : 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 : 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 04:52:42 PM UTC 2026
% Result : Unsatisfiable 5.36s 5.68s
% Output : CNFRefutation 5.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of clauses : 57 ( 37 unt; 0 nHn; 28 RR)
% Number of literals : 97 ( 0 equ; 47 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 142 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_equation,negated_conjecture,
~ equalish(add(a,subtract(b,c)),add(subtract(a,c),b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(commutativity2,axiom,
equalish(subtract(add(X1,X2),X3),add(subtract(X1,X3),X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',commutativity2) ).
cnf(commutativity1,axiom,
equalish(add(subtract(X1,X2),X3),subtract(add(X1,X3),X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',commutativity1) ).
cnf(associativity_of_addition,axiom,
equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',associativity_of_addition) ).
cnf(subtract_substitution1,axiom,
( equalish(X3,subtract(X2,X4))
| ~ equalish(X1,X2)
| ~ equalish(X3,subtract(X1,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',subtract_substitution1) ).
cnf(subtract_substitution2,axiom,
( equalish(X3,subtract(X4,X2))
| ~ equalish(X1,X2)
| ~ equalish(X3,subtract(X4,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',subtract_substitution2) ).
cnf(add_substitution1,axiom,
( equalish(X3,add(X2,X4))
| ~ equalish(X1,X2)
| ~ equalish(X3,add(X1,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',add_substitution1) ).
cnf(add_substitution2,axiom,
( equalish(X3,add(X4,X2))
| ~ equalish(X1,X2)
| ~ equalish(X3,add(X4,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',add_substitution2) ).
cnf(addition_inverts_subtraction1,axiom,
equalish(subtract(add(X1,X2),X2),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',addition_inverts_subtraction1) ).
cnf(addition_inverts_subtraction2,axiom,
equalish(X1,subtract(add(X1,X2),X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',addition_inverts_subtraction2) ).
cnf(commutativity_of_addition,axiom,
equalish(add(X1,X2),add(X2,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',commutativity_of_addition) ).
cnf(transitivity,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',transitivity) ).
cnf(reflexivity,axiom,
equalish(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',reflexivity) ).
cnf(i_0_13,negated_conjecture,
~ equalish(add(a,subtract(b,c)),add(subtract(a,c),b)),
prove_equation,
[final] ).
cnf(i_0_14,axiom,
equalish(subtract(add(X1,X2),X3),add(subtract(X1,X3),X2)),
commutativity2,
[final] ).
cnf(i_0_15,axiom,
equalish(add(subtract(X1,X2),X3),subtract(add(X1,X3),X2)),
commutativity1,
[final] ).
cnf(i_0_16,axiom,
equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3)),
associativity_of_addition,
[final] ).
cnf(i_0_17,axiom,
( equalish(X3,subtract(X2,X4))
| ~ equalish(X1,X2)
| ~ equalish(X3,subtract(X1,X4)) ),
subtract_substitution1,
[final] ).
cnf(i_0_18,axiom,
( equalish(X3,subtract(X4,X2))
| ~ equalish(X1,X2)
| ~ equalish(X3,subtract(X4,X1)) ),
subtract_substitution2,
[final] ).
cnf(i_0_19,axiom,
( equalish(X3,add(X2,X4))
| ~ equalish(X1,X2)
| ~ equalish(X3,add(X1,X4)) ),
add_substitution1,
[final] ).
cnf(i_0_20,axiom,
( equalish(X3,add(X4,X2))
| ~ equalish(X1,X2)
| ~ equalish(X3,add(X4,X1)) ),
add_substitution2,
[final] ).
cnf(i_0_21,axiom,
equalish(subtract(add(X1,X2),X2),X1),
addition_inverts_subtraction1,
[final] ).
cnf(i_0_22,axiom,
equalish(X1,subtract(add(X1,X2),X2)),
addition_inverts_subtraction2,
[final] ).
cnf(i_0_23,axiom,
equalish(add(X1,X2),add(X2,X1)),
commutativity_of_addition,
[final] ).
cnf(i_0_24,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
transitivity,
[final] ).
cnf(i_0_25,axiom,
equalish(X1,X1),
reflexivity,
[final] ).
cnf(i_0_26,plain,
equalish(add(add(X1,X2),X3),add(add(X2,X1),X3)),
inference(scs_inference,[],[i_0_25,i_0_23,i_0_19]) ).
cnf(i_0_27,plain,
equalish(X1,X1),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_28,plain,
( ~ equalish(X1,add(X2,X3))
| equalish(X1,add(X4,X3))
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_29,plain,
equalish(subtract(add(X1,X2),X3),subtract(add(X2,X1),X3)),
inference(scs_inference,[],[i_0_25,i_0_27,i_0_23,i_0_19,i_0_17]) ).
cnf(i_0_30,plain,
equalish(X1,X1),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_31,plain,
( ~ equalish(X1,subtract(X2,X3))
| equalish(X1,subtract(X4,X3))
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_32,plain,
equalish(subtract(X1,add(X2,X3)),subtract(X1,add(X3,X2))),
inference(scs_inference,[],[i_0_25,i_0_27,i_0_30,i_0_23,i_0_19,i_0_17,i_0_18]) ).
cnf(i_0_33,plain,
equalish(X1,X1),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_34,plain,
( ~ equalish(X1,subtract(X2,X3))
| equalish(X1,subtract(X2,X4))
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_18]) ).
cnf(i_0_35,plain,
equalish(add(X1,add(X2,X3)),add(X1,add(X3,X2))),
inference(scs_inference,[],[i_0_25,i_0_27,i_0_30,i_0_33,i_0_23,i_0_19,i_0_17,i_0_18,i_0_20]) ).
cnf(i_0_36,plain,
equalish(X1,X1),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_37,plain,
( ~ equalish(X1,add(X2,X3))
| equalish(X1,add(X2,X4))
| ~ equalish(X3,X4) ),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_38,plain,
~ equalish(add(a,subtract(b,c)),add(b,subtract(a,c))),
inference(scs_inference,[],[i_0_13,i_0_25,i_0_27,i_0_30,i_0_33,i_0_23,i_0_19,i_0_17,i_0_18,i_0_20,i_0_24]) ).
cnf(i_0_39,plain,
equalish(add(X1,X2),add(X2,X1)),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_40,plain,
( ~ equalish(X1,X2)
| equalish(X3,X2)
| ~ equalish(X3,X1) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_41,plain,
equalish(add(X1,X2),subtract(add(add(X2,X1),X3),X3)),
inference(scs_inference,[],[i_0_26,i_0_22,i_0_17]) ).
cnf(i_0_42,plain,
equalish(X1,subtract(add(X1,X2),X2)),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_43,plain,
( ~ equalish(X1,subtract(X2,X3))
| equalish(X1,subtract(X4,X3))
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_44,plain,
~ equalish(add(a,subtract(b,c)),subtract(add(a,b),c)),
inference(scs_inference,[],[i_0_13,i_0_26,i_0_14,i_0_22,i_0_17,i_0_24]) ).
cnf(i_0_45,plain,
equalish(subtract(add(X1,X2),X3),add(subtract(X1,X3),X2)),
inference(rename_variables,[],[i_0_14]) ).
cnf(i_0_46,plain,
( ~ equalish(X1,X2)
| equalish(X3,X2)
| ~ equalish(X3,X1) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_47,plain,
~ equalish(add(add(subtract(b,c),a),c),add(a,b)),
inference(scs_inference,[],[i_0_41,i_0_44,i_0_17]) ).
cnf(i_0_48,plain,
equalish(add(X1,X2),subtract(add(add(X2,X1),X3),X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_49,plain,
( ~ equalish(X1,subtract(X2,X3))
| equalish(X1,subtract(X4,X3))
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_50,plain,
~ equalish(add(a,subtract(b,c)),subtract(add(b,a),c)),
inference(scs_inference,[],[i_0_29,i_0_41,i_0_44,i_0_17,i_0_24]) ).
cnf(i_0_51,plain,
equalish(subtract(add(X1,X2),X3),subtract(add(X2,X1),X3)),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_52,plain,
( ~ equalish(X1,X2)
| equalish(X3,X2)
| ~ equalish(X3,X1) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_53,plain,
~ equalish(add(add(subtract(b,c),a),c),add(b,a)),
inference(scs_inference,[],[i_0_50,i_0_41,i_0_17]) ).
cnf(i_0_54,plain,
equalish(add(X1,X2),subtract(add(add(X2,X1),X3),X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_55,plain,
( ~ equalish(X1,subtract(X2,X3))
| equalish(X1,subtract(X4,X3))
| ~ equalish(X2,X4) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_56,plain,
$false,
inference(scs_inference,[],[i_0_50,i_0_15,i_0_41,i_0_23,i_0_17,i_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM003-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue May 5 00:05:07 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.33 % start to proof: theBenchmark
% 5.36/5.68 % Version : CSE_E---1.7
% 5.36/5.68 % Problem : theBenchmark.p
% 5.36/5.68 % SZS status Unsatisfiable for theBenchmark.p
% 5.36/5.68 % SZS output start CNFRefutation
% See solution above
% 5.49/5.74 % Total time : 5.351s
%------------------------------------------------------------------------------