%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP777-10 : TPTP v9.2.1. Released v8.1.0.
% 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 : n024.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 04:27:15 PM UTC 2026
% Result : Unsatisfiable 3.16s 2.89s
% Output : CNFRefutation 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of clauses : 77 ( 77 unt; 0 nHn; 36 RR)
% Number of literals : 77 ( 76 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 97 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos05,axiom,
product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
cnf(sos06,axiom,
product(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
cnf(sos09,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
cnf(sos03,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
cnf(sos01,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
cnf(sos07,axiom,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
cnf(sos04,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
cnf(sos02,axiom,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
cnf(goal,negated_conjecture,
bigC(a,b,x0) != bigC(c,c,x0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(sos08,axiom,
bigC(X1,X2,X3) = product(product(X1,X2),product(X3,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
cnf(c_0_10,axiom,
product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)),
sos05 ).
cnf(c_0_11,axiom,
product(X1,X1) = X1,
sos06 ).
cnf(c_0_12,plain,
product(product(X1,X2),product(X1,X3)) = product(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,axiom,
product(product(a,c),product(c,b)) = product(a,b),
sos09 ).
cnf(c_0_14,plain,
product(product(product(a,c),X1),product(a,b)) = product(product(a,c),product(X1,product(c,b))),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_16,axiom,
quotient(product(X1,X2),X2) = X1,
sos03 ).
cnf(c_0_17,axiom,
difference(X1,product(X1,X2)) = X2,
sos01 ).
cnf(c_0_18,plain,
product(a,product(product(c,a),b)) = product(a,product(c,product(c,b))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_12]),c_0_12]) ).
cnf(c_0_19,axiom,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
sos07 ).
cnf(c_0_20,plain,
product(product(X1,X2),product(X3,X2)) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_21,plain,
quotient(product(X1,product(X2,X1)),X1) = product(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_22,plain,
product(product(c,a),b) = product(c,product(c,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_17]) ).
cnf(c_0_23,plain,
product(product(product(X1,X2),product(X3,X4)),product(X5,X6)) = product(product(product(X1,X3),X5),product(product(X2,X4),X6)),
inference(spm,[status(thm)],[c_0_10,c_0_10]) ).
cnf(c_0_24,plain,
product(product(product(a,c),b),product(product(c,b),product(product(c,a),product(b,c)))) = product(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_13]),c_0_20]),c_0_10]) ).
cnf(c_0_25,plain,
product(product(product(a,c),X1),product(product(c,b),X2)) = product(product(a,b),product(X1,X2)),
inference(spm,[status(thm)],[c_0_10,c_0_13]) ).
cnf(c_0_26,plain,
product(product(c,a),product(b,c)) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_13]),c_0_20]),c_0_22]),c_0_16]),c_0_10]) ).
cnf(c_0_27,plain,
product(product(product(product(c,a),product(b,c)),a),product(a,b)) = product(a,c),
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_19,c_0_13]),c_0_10]),c_0_23]),c_0_12]),c_0_23]),c_0_10]),c_0_13]) ).
cnf(c_0_28,plain,
product(product(a,b),product(b,product(product(c,a),product(b,c)))) = product(c,b),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
product(product(product(c,a),X1),product(b,c)) = product(c,product(X1,product(b,c))),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_30,plain,
product(product(c,a),product(a,b)) = product(a,c),
inference(rw,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_31,plain,
product(product(a,b),product(b,c)) = product(c,b),
inference(rw,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_32,plain,
product(product(a,c),product(product(c,a),product(b,c))) = product(a,product(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_12]),c_0_10]) ).
cnf(c_0_33,plain,
product(product(X1,c),product(b,product(c,b))) = product(product(X1,product(c,a)),b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_22]),c_0_10]) ).
cnf(c_0_34,plain,
product(product(a,b),c) = product(c,product(c,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_20]),c_0_31]) ).
cnf(c_0_35,plain,
product(product(a,c),c) = product(a,product(b,c)),
inference(rw,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_36,plain,
product(product(X1,X2),product(product(X3,X4),product(X5,X6))) = product(product(X1,product(X3,X5)),product(X2,product(X4,X6))),
inference(spm,[status(thm)],[c_0_10,c_0_10]) ).
cnf(c_0_37,plain,
product(product(product(a,c),product(b,a)),b) = product(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_20]),c_0_12]),c_0_11]),c_0_10]) ).
cnf(c_0_38,plain,
product(product(a,c),product(product(b,c),product(c,a))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_35]),c_0_36]) ).
cnf(c_0_39,plain,
product(product(a,c),product(b,a)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_37]),c_0_16]) ).
cnf(c_0_40,plain,
difference(product(a,c),c) = product(product(b,c),product(c,a)),
inference(spm,[status(thm)],[c_0_17,c_0_38]) ).
cnf(c_0_41,axiom,
product(quotient(X1,X2),X2) = X1,
sos04 ).
cnf(c_0_42,plain,
product(product(b,c),product(c,a)) = product(b,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_39]),c_0_40]) ).
cnf(c_0_43,plain,
product(product(X1,quotient(X2,X3)),X3) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_20,c_0_41]) ).
cnf(c_0_44,axiom,
product(X1,difference(X1,X2)) = X2,
sos02 ).
cnf(c_0_45,plain,
product(product(X1,X2),product(X2,product(X2,quotient(X1,X2)))) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_41]) ).
cnf(c_0_46,plain,
product(product(b,c),c) = product(b,product(a,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_42]),c_0_12]),c_0_26]) ).
cnf(c_0_47,plain,
product(product(X1,product(a,c)),product(X2,product(c,b))) = product(product(X1,X2),product(a,b)),
inference(spm,[status(thm)],[c_0_10,c_0_13]) ).
cnf(c_0_48,plain,
quotient(product(product(X1,X2),X3),X2) = product(X1,quotient(X3,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_43]) ).
cnf(c_0_49,plain,
product(X1,product(X2,difference(X1,X3))) = product(product(X1,X2),X3),
inference(spm,[status(thm)],[c_0_12,c_0_44]) ).
cnf(c_0_50,plain,
product(product(c,a),product(product(b,c),X1)) = product(c,product(product(c,a),X1)),
inference(spm,[status(thm)],[c_0_12,c_0_26]) ).
cnf(c_0_51,plain,
product(product(b,c),product(a,b)) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_16]),c_0_47]) ).
cnf(c_0_52,plain,
quotient(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_53,plain,
product(a,quotient(product(b,c),b)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_31]),c_0_16]) ).
cnf(c_0_54,plain,
difference(X1,product(product(X1,X2),X3)) = product(X2,difference(X1,X3)),
inference(spm,[status(thm)],[c_0_17,c_0_49]) ).
cnf(c_0_55,plain,
product(product(c,b),a) = product(c,product(c,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_42]),c_0_20]),c_0_12]),c_0_11]) ).
cnf(c_0_56,plain,
product(b,quotient(product(a,b),c)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_51]),c_0_52]) ).
cnf(c_0_57,plain,
quotient(product(b,c),b) = difference(a,c),
inference(spm,[status(thm)],[c_0_17,c_0_53]) ).
cnf(c_0_58,plain,
product(product(X1,X2),product(X3,difference(X2,X4))) = product(product(X1,X3),X4),
inference(spm,[status(thm)],[c_0_10,c_0_44]) ).
cnf(c_0_59,plain,
product(b,difference(c,a)) = product(c,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_17]) ).
cnf(c_0_60,plain,
quotient(product(a,b),c) = difference(b,c),
inference(spm,[status(thm)],[c_0_17,c_0_56]) ).
cnf(c_0_61,plain,
product(product(X1,X2),product(difference(X1,X3),X4)) = product(X3,product(X2,X4)),
inference(spm,[status(thm)],[c_0_10,c_0_44]) ).
cnf(c_0_62,plain,
product(difference(a,c),b) = product(b,c),
inference(spm,[status(thm)],[c_0_41,c_0_57]) ).
cnf(c_0_63,plain,
product(product(X1,c),product(c,a)) = product(product(X1,b),a),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,plain,
product(difference(b,c),c) = product(a,b),
inference(spm,[status(thm)],[c_0_41,c_0_60]) ).
cnf(c_0_65,plain,
product(product(X1,quotient(X2,X3)),product(X4,X3)) = product(product(X1,X4),X2),
inference(spm,[status(thm)],[c_0_10,c_0_41]) ).
cnf(c_0_66,plain,
product(product(a,X1),product(b,c)) = product(c,product(X1,b)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,plain,
product(product(difference(b,c),b),a) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_10]),c_0_39]) ).
cnf(c_0_68,negated_conjecture,
bigC(a,b,x0) != bigC(c,c,x0),
goal ).
cnf(c_0_69,axiom,
bigC(X1,X2,X3) = product(product(X1,X2),product(X3,X1)),
sos08 ).
cnf(c_0_70,plain,
product(c,product(quotient(X1,c),b)) = product(product(a,b),X1),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,plain,
product(difference(b,c),b) = quotient(c,a),
inference(spm,[status(thm)],[c_0_16,c_0_67]) ).
cnf(c_0_72,negated_conjecture,
product(product(c,c),product(x0,c)) != product(product(a,b),product(x0,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69]),c_0_69]) ).
cnf(c_0_73,plain,
product(c,quotient(c,a)) = product(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_60]),c_0_71]),c_0_12]),c_0_11]) ).
cnf(c_0_74,negated_conjecture,
product(product(a,b),product(x0,a)) != product(c,product(x0,c)),
inference(rw,[status(thm)],[c_0_72,c_0_11]) ).
cnf(c_0_75,plain,
product(product(a,b),product(X1,a)) = product(c,product(X1,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_73]),c_0_15]) ).
cnf(c_0_76,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP777-10 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 14:05:11 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 3.16/2.89 % Version : CSE_E---1.7
% 3.16/2.89 % Problem : theBenchmark.p
% 3.16/2.89 % SZS status Unsatisfiable for theBenchmark.p
% 3.16/2.89 % SZS output start CNFRefutation
% See solution above
% 3.27/2.90 % Total time : 2.362s
%------------------------------------------------------------------------------