%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO020-1 : TPTP v9.2.1. Released v2.2.0.
% 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 : n001.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 04:11:09 PM UTC 2026
% Result : Unsatisfiable 3.90s 3.21s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 4
% Syntax : Number of clauses : 58 ( 41 unt; 0 nHn; 20 RR)
% Number of literals : 77 ( 76 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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 : 110 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(frink2,axiom,
( add(add(add(X1,X2),X3),inverse(X4)) = n0
| add(add(add(X1,X2),X3),X4) != add(add(X2,X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',frink2) ).
cnf(frink1,axiom,
add(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',frink1) ).
cnf(frink3,axiom,
( add(add(add(X1,X2),X3),X4) = add(add(X2,X3),X1)
| add(add(add(X1,X2),X3),inverse(X4)) != n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',frink3) ).
cnf(prove_huntington,negated_conjecture,
( add(inverse(add(a,inverse(b))),inverse(add(inverse(a),inverse(b)))) != b
| add(add(a,b),c) != add(a,add(b,c))
| add(b,a) != add(a,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_huntington) ).
cnf(c_0_4,axiom,
( add(add(add(X1,X2),X3),inverse(X4)) = n0
| add(add(add(X1,X2),X3),X4) != add(add(X2,X3),X1) ),
frink2 ).
cnf(c_0_5,axiom,
add(X1,X1) = X1,
frink1 ).
cnf(c_0_6,plain,
( add(add(X1,X2),inverse(X3)) = n0
| add(add(X1,X2),X3) != add(add(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
( add(X1,inverse(X2)) = n0
| add(X1,X2) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_5]),c_0_5]) ).
cnf(c_0_8,axiom,
( add(add(add(X1,X2),X3),X4) = add(add(X2,X3),X1)
| add(add(add(X1,X2),X3),inverse(X4)) != n0 ),
frink3 ).
cnf(c_0_9,plain,
add(add(X1,X2),inverse(X1)) = n0,
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
add(X1,inverse(X1)) = n0,
inference(spm,[status(thm)],[c_0_7,c_0_5]) ).
cnf(c_0_11,plain,
( add(add(X1,X2),X3) = add(add(X1,X2),X1)
| add(add(X1,X2),inverse(X3)) != n0 ),
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_12,plain,
add(n0,inverse(X1)) = n0,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( add(add(X1,X2),X3) = add(add(X2,add(X1,X2)),X1)
| add(add(X1,X2),inverse(X3)) != n0 ),
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_14,plain,
add(n0,X1) = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_5]),c_0_12])]) ).
cnf(c_0_15,plain,
add(add(X1,add(X2,X1)),X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_10]),c_0_5]) ).
cnf(c_0_16,plain,
add(add(X1,X2),n0) = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_14]),c_0_14]),c_0_14]),c_0_14]),c_0_14])]) ).
cnf(c_0_17,plain,
( add(X1,X2) = X1
| add(X1,inverse(X2)) != n0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_5]),c_0_5]) ).
cnf(c_0_18,plain,
add(inverse(X1),X1) = n0,
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_19,plain,
add(X1,n0) = n0,
inference(spm,[status(thm)],[c_0_16,c_0_5]) ).
cnf(c_0_20,plain,
add(inverse(inverse(X1)),X1) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
inverse(inverse(n0)) = n0,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
add(X1,inverse(n0)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_19])]) ).
cnf(c_0_23,plain,
( add(add(X1,X2),X3) = n0
| add(add(X3,X1),X2) != n0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_22]),c_0_19]) ).
cnf(c_0_24,plain,
add(add(X1,inverse(X2)),X2) = n0,
inference(spm,[status(thm)],[c_0_23,c_0_9]) ).
cnf(c_0_25,plain,
( add(X1,X2) = n0
| add(X2,X1) != n0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_22]) ).
cnf(c_0_26,plain,
add(inverse(inverse(inverse(X1))),X1) = n0,
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_27,plain,
add(X1,inverse(inverse(inverse(X1)))) = n0,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_29,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_28]),c_0_20]),c_0_20]) ).
cnf(c_0_30,plain,
add(add(inverse(X1),X2),X1) = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_10]),c_0_14])]) ).
cnf(c_0_31,plain,
( add(X1,inverse(X2)) = X1
| add(X1,X2) != n0 ),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_32,plain,
add(add(X1,X2),inverse(X2)) = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_30]),c_0_14]),c_0_14])]) ).
cnf(c_0_33,plain,
add(add(X1,X2),X2) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29]) ).
cnf(c_0_34,plain,
add(add(X1,X2),X3) = add(add(X2,X3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_10]),c_0_5]) ).
cnf(c_0_35,plain,
add(add(X1,X2),X1) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_10]),c_0_5]) ).
cnf(c_0_36,plain,
add(X1,X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_37,plain,
( add(add(X1,X2),X3) = n0
| add(add(X2,X3),X1) != n0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_10]),c_0_29]),c_0_5]) ).
cnf(c_0_38,plain,
add(X1,add(X2,inverse(X1))) = n0,
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_39,plain,
( add(add(X1,X2),X3) = add(X2,X1)
| add(add(X1,X2),inverse(X3)) != n0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_22]),c_0_22]) ).
cnf(c_0_40,plain,
add(add(X1,X2),X3) = add(X2,add(X3,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_36]) ).
cnf(c_0_41,plain,
add(add(X1,X2),inverse(add(X2,X1))) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_10]),c_0_36]),c_0_34]) ).
cnf(c_0_42,plain,
add(X1,inverse(add(X2,inverse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_38]) ).
cnf(c_0_43,plain,
add(inverse(X1),add(X1,X2)) = n0,
inference(spm,[status(thm)],[c_0_25,c_0_9]) ).
cnf(c_0_44,plain,
( add(X1,add(X2,X3)) = add(X1,X3)
| add(X1,add(inverse(X2),X3)) != n0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_40]) ).
cnf(c_0_45,plain,
add(X1,add(X2,inverse(add(X1,X2)))) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_40]),c_0_36]) ).
cnf(c_0_46,plain,
add(inverse(add(X1,inverse(X2))),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_42]),c_0_33]) ).
cnf(c_0_47,plain,
add(inverse(X1),inverse(add(X1,X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_31,c_0_43]) ).
cnf(c_0_48,plain,
add(X1,inverse(add(X1,inverse(X2)))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_42]) ).
cnf(c_0_49,plain,
add(X1,add(X1,X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_29]) ).
cnf(c_0_50,plain,
add(X1,inverse(add(X1,X2))) = add(X1,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_48]),c_0_49]) ).
cnf(c_0_51,plain,
add(inverse(X1),add(X2,X1)) = n0,
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_52,negated_conjecture,
( add(inverse(add(a,inverse(b))),inverse(add(inverse(a),inverse(b)))) != b
| add(add(a,b),c) != add(a,add(b,c))
| add(b,a) != add(a,b) ),
prove_huntington ).
cnf(c_0_53,plain,
add(X1,inverse(add(X2,X1))) = add(X1,inverse(X2)),
inference(spm,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_54,plain,
add(inverse(X1),inverse(add(X2,X1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_31,c_0_51]) ).
cnf(c_0_55,negated_conjecture,
add(inverse(add(a,inverse(b))),inverse(add(inverse(b),inverse(a)))) != b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_34]),c_0_36]),c_0_36]),c_0_36])]) ).
cnf(c_0_56,plain,
add(inverse(add(X1,X2)),inverse(add(X2,inverse(X1)))) = inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_53]),c_0_36]),c_0_54]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO020-1 : TPTP v9.2.1. Released v2.2.0.
% 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 : n001.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 10:47:03 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.90/3.21 % Version : CSE_E---1.7
% 3.90/3.21 % Problem : theBenchmark.p
% 3.90/3.21 % SZS status Unsatisfiable for theBenchmark.p
% 3.90/3.21 % SZS output start CNFRefutation
% See solution above
% 3.90/3.22 % Total time : 2.372s
%------------------------------------------------------------------------------