%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP772-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:41:13 PM UTC 2026
% Result : Unsatisfiable 0.75s 0.51s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of clauses : 78 ( 78 unt; 0 nHn; 4 RR)
% Number of literals : 78 ( 77 equ; 3 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 : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 179 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos08,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
cnf(sos07,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
cnf(sos03,axiom,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
cnf(sos24,axiom,
product(product(X1,X2),c(X2,X1)) = product(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos24) ).
cnf(sos26,axiom,
product(product(X1,X2),c(X3,X4)) = product(X1,product(X2,c(X3,X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos26) ).
cnf(sos06,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
cnf(sos02,axiom,
product(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
cnf(sos01,axiom,
product(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
cnf(sos04,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
cnf(sos05,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
cnf(sos11,axiom,
product(i(X1),X1) = product(X1,j(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).
cnf(sos09,axiom,
i(X1) = difference(X1,one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
cnf(sos10,axiom,
j(X1) = quotient(one,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
cnf(sos28,axiom,
product(product(X1,X2),a(X3,X4,X5)) = product(X1,product(X2,a(X3,X4,X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos28) ).
cnf(sos29,axiom,
product(a(X1,X2,X3),difference(X3,product(a(X3,X1,X2),X3))) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos29) ).
cnf(sos27,axiom,
product(a(X1,X2,X3),product(X4,X5)) = product(product(a(X1,X2,X3),X4),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos27) ).
cnf(sos31,axiom,
a(i(X1),X2,X3) = a(j(X1),X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos31) ).
cnf(sos32,axiom,
a(j(X1),X2,X3) = a(X2,X3,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos32) ).
cnf(sos30,axiom,
a(X1,i(X2),X3) = a(X1,j(X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos30) ).
cnf(goals,negated_conjecture,
a(x0,x1,x1) != a(x1,x1,x0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_20,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
sos08 ).
cnf(c_0_21,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
sos07 ).
cnf(c_0_22,plain,
quotient(difference(X1,product(product(X1,X2),X3)),X3) = difference(product(X3,X1),product(X3,product(X1,X2))),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,axiom,
product(X1,difference(X1,X2)) = X2,
sos03 ).
cnf(c_0_24,axiom,
product(product(X1,X2),c(X2,X1)) = product(X2,X1),
sos24 ).
cnf(c_0_25,axiom,
product(product(X1,X2),c(X3,X4)) = product(X1,product(X2,c(X3,X4))),
sos26 ).
cnf(c_0_26,axiom,
product(quotient(X1,X2),X2) = X1,
sos06 ).
cnf(c_0_27,plain,
quotient(difference(X1,product(X2,X3)),X3) = difference(product(X3,X1),product(X3,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,axiom,
product(one,X1) = X1,
sos02 ).
cnf(c_0_29,axiom,
product(X1,one) = X1,
sos01 ).
cnf(c_0_30,axiom,
difference(X1,product(X1,X2)) = X2,
sos04 ).
cnf(c_0_31,plain,
product(X1,product(X2,c(X2,X1))) = product(X2,X1),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
product(quotient(X1,X2),product(X2,c(X3,X4))) = product(X1,c(X3,X4)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,axiom,
quotient(product(X1,X2),X2) = X1,
sos05 ).
cnf(c_0_34,plain,
quotient(difference(X1,X2),X2) = difference(product(X2,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_35,plain,
difference(X1,X1) = one,
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_36,plain,
product(X1,c(X2,quotient(X1,X2))) = product(X2,quotient(X1,X2)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
quotient(X1,difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_38,axiom,
product(i(X1),X1) = product(X1,j(X1)),
sos11 ).
cnf(c_0_39,axiom,
i(X1) = difference(X1,one),
sos09 ).
cnf(c_0_40,axiom,
j(X1) = quotient(one,X1),
sos10 ).
cnf(c_0_41,plain,
difference(product(X1,X1),X1) = quotient(one,X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
product(X1,c(difference(X2,X1),X2)) = product(difference(X2,X1),X2),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,plain,
product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_44,plain,
product(product(X1,X1),quotient(one,X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_41]) ).
cnf(c_0_45,plain,
difference(X1,product(X2,X1)) = product(X2,c(X2,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_46,plain,
c(difference(X1,one),X1) = product(difference(X1,one),X1),
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_47,plain,
difference(X1,product(difference(X1,one),X1)) = quotient(one,X1),
inference(spm,[status(thm)],[c_0_30,c_0_43]) ).
cnf(c_0_48,axiom,
product(product(X1,X2),a(X3,X4,X5)) = product(X1,product(X2,a(X3,X4,X5))),
sos28 ).
cnf(c_0_49,plain,
product(product(difference(X1,one),difference(X1,one)),X1) = difference(X1,one),
inference(spm,[status(thm)],[c_0_44,c_0_37]) ).
cnf(c_0_50,plain,
product(difference(X1,one),product(difference(X1,one),X1)) = quotient(one,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_51,axiom,
product(a(X1,X2,X3),difference(X3,product(a(X3,X1,X2),X3))) = one,
sos29 ).
cnf(c_0_52,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_53,plain,
quotient(one,a(X1,X2,X3)) = difference(a(X1,X2,X3),one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_54,plain,
difference(X1,product(a(X1,X2,X3),X1)) = difference(a(X2,X3,X1),one),
inference(spm,[status(thm)],[c_0_30,c_0_51]) ).
cnf(c_0_55,plain,
quotient(product(X1,product(difference(X2,one),X2)),quotient(one,X2)) = difference(quotient(one,X2),product(product(quotient(one,X2),X1),X2)),
inference(spm,[status(thm)],[c_0_21,c_0_43]) ).
cnf(c_0_56,plain,
difference(difference(a(X1,X2,X3),one),one) = a(X1,X2,X3),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,axiom,
product(a(X1,X2,X3),product(X4,X5)) = product(product(a(X1,X2,X3),X4),X5),
sos27 ).
cnf(c_0_58,axiom,
a(i(X1),X2,X3) = a(j(X1),X2,X3),
sos31 ).
cnf(c_0_59,axiom,
a(j(X1),X2,X3) = a(X2,X3,X1),
sos32 ).
cnf(c_0_60,plain,
product(X1,difference(a(X2,X3,X1),one)) = product(a(X1,X2,X3),X1),
inference(spm,[status(thm)],[c_0_23,c_0_54]) ).
cnf(c_0_61,plain,
product(X1,difference(a(X2,X3,X4),one)) = quotient(X1,a(X2,X3,X4)),
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_55,c_0_56]),c_0_23]),c_0_29]),c_0_37]),c_0_37]),c_0_37]),c_0_57]),c_0_30]) ).
cnf(c_0_62,axiom,
a(X1,i(X2),X3) = a(X1,j(X2),X3),
sos30 ).
cnf(c_0_63,plain,
a(quotient(one,X1),X2,X3) = a(difference(X1,one),X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_39]),c_0_40]) ).
cnf(c_0_64,plain,
a(quotient(one,X1),X2,X3) = a(X2,X3,X1),
inference(rw,[status(thm)],[c_0_59,c_0_40]) ).
cnf(c_0_65,plain,
quotient(X1,a(X2,X3,X1)) = product(a(X1,X2,X3),X1),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,plain,
a(X1,quotient(one,X2),X3) = a(X1,difference(X2,one),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_39]),c_0_40]) ).
cnf(c_0_67,plain,
a(difference(X1,one),X2,X3) = a(X2,X3,X1),
inference(rw,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,plain,
product(a(X1,difference(X2,one),X3),X1) = quotient(X1,a(X3,X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_64]),c_0_66]) ).
cnf(c_0_69,plain,
a(X1,X2,quotient(one,X3)) = a(X3,X1,X2),
inference(spm,[status(thm)],[c_0_67,c_0_52]) ).
cnf(c_0_70,plain,
a(X1,X2,difference(X3,one)) = a(X3,X1,X2),
inference(spm,[status(thm)],[c_0_64,c_0_37]) ).
cnf(c_0_71,plain,
quotient(X1,a(X1,X2,X3)) = product(a(X2,X3,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_64]) ).
cnf(c_0_72,negated_conjecture,
a(x0,x1,x1) != a(x1,x1,x0),
inference(fof_simplification,[status(thm)],[goals]) ).
cnf(c_0_73,plain,
difference(product(a(X1,X2,X3),X1),X1) = a(X2,X3,X1),
inference(spm,[status(thm)],[c_0_52,c_0_65]) ).
cnf(c_0_74,plain,
difference(product(a(X1,X2,X3),X3),X3) = a(X3,X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
a(x0,x1,x1) != a(x1,x1,x0),
c_0_72 ).
cnf(c_0_76,plain,
a(X1,X1,X2) = a(X2,X1,X1),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP772-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:39:20 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.75/0.51 % Version: 3.5.1
% 0.75/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.75/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.75/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.75/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.75/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.75/0.51 % Starting sh5l with 300s (1) cores
% 0.75/0.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1451554 completed with status 0
% 0.75/0.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.75/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.75/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.75/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.75/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.75/0.51 % No SInE strategy applied
% 0.75/0.51 % Search class: FUUPM-FFMF32-MFFFFFNN
% 0.75/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.75/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.75/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.75/0.51 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 437s (1) cores
% 0.75/0.51 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 0.75/0.51 % Starting G-E--_208_B02_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 0.75/0.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1451561 completed with status 0
% 0.75/0.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.75/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.75/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.75/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.75/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.75/0.51 % No SInE strategy applied
% 0.75/0.51 % Search class: FUUPM-FFMF32-MFFFFFNN
% 0.75/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.75/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.75/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.75/0.51 % Preprocessing time : 0.001 s
% 0.75/0.51 % Presaturation interreduction done
% 0.75/0.51
% 0.75/0.51 % Proof found!
% 0.75/0.51 % SZS status Unsatisfiable
% 0.75/0.51 % SZS output start CNFRefutation
% See solution above
% 0.75/0.51 % Parsed axioms : 33
% 0.75/0.51 % Removed by relevancy pruning/SinE : 0
% 0.75/0.51 % Initial clauses : 33
% 0.75/0.51 % Removed in clause preprocessing : 4
% 0.75/0.51 % Initial clauses in saturation : 29
% 0.75/0.51 % Processed clauses : 581
% 0.75/0.51 % ...of these trivial : 248
% 0.75/0.51 % ...subsumed : 36
% 0.75/0.51 % ...remaining for further processing : 297
% 0.75/0.51 % Other redundant clauses eliminated : 0
% 0.75/0.51 % Clauses deleted for lack of memory : 0
% 0.75/0.51 % Backward-subsumed : 0
% 0.75/0.51 % Backward-rewritten : 73
% 0.75/0.51 % Generated clauses : 13285
% 0.75/0.51 % ...of the previous two non-redundant : 8276
% 0.75/0.51 % ...aggressively subsumed : 0
% 0.75/0.51 % Contextual simplify-reflections : 0
% 0.75/0.51 % Paramodulations : 13285
% 0.75/0.51 % Factorizations : 0
% 0.75/0.51 % NegExts : 0
% 0.75/0.51 % Equation resolutions : 0
% 0.75/0.51 % Disequality decompositions : 0
% 0.75/0.51 % Total rewrite steps : 29385
% 0.75/0.51 % ...of those cached : 25512
% 0.75/0.51 % Propositional unsat checks : 0
% 0.75/0.51 % Propositional check models : 0
% 0.75/0.51 % Propositional check unsatisfiable : 0
% 0.75/0.51 % Propositional clauses : 0
% 0.75/0.51 % Propositional clauses after purity: 0
% 0.75/0.51 % Propositional unsat core size : 0
% 0.75/0.51 % Propositional preprocessing time : 0.000
% 0.75/0.51 % Propositional encoding time : 0.000
% 0.75/0.51 % Propositional solver time : 0.000
% 0.75/0.51 % Success case prop preproc time : 0.000
% 0.75/0.51 % Success case prop encoding time : 0.000
% 0.75/0.51 % Success case prop solver time : 0.000
% 0.75/0.51 % Current number of processed clauses : 195
% 0.75/0.51 % Positive orientable unit clauses : 190
% 0.75/0.51 % Positive unorientable unit clauses: 5
% 0.75/0.51 % Negative unit clauses : 0
% 0.75/0.51 % Non-unit-clauses : 0
% 0.75/0.51 % Current number of unprocessed clauses: 7588
% 0.75/0.51 % ...number of literals in the above : 7588
% 0.75/0.51 % Current number of archived formulas : 0
% 0.75/0.51 % Current number of archived clauses : 106
% 0.75/0.51 % Clause-clause subsumption calls (NU) : 0
% 0.75/0.51 % Rec. Clause-clause subsumption calls : 0
% 0.75/0.51 % Non-unit clause-clause subsumptions : 0
% 0.75/0.51 % Unit Clause-clause subsumption calls : 36
% 0.75/0.51 % Rewrite failures with RHS unbound : 0
% 0.75/0.51 % BW rewrite match attempts : 371
% 0.75/0.51 % BW rewrite match successes : 70
% 0.75/0.51 % Condensation attempts : 0
% 0.75/0.51 % Condensation successes : 0
% 0.75/0.51 % Termbank termtop insertions : 191435
% 0.75/0.51 % Search garbage collected termcells : 2
% 0.75/0.51
% 0.75/0.51 % -------------------------------------------------
% 0.75/0.51 % User time : 0.087 s
% 0.75/0.51 % System time : 0.014 s
% 0.75/0.51 % Total time : 0.101 s
% 0.75/0.51 % Maximum resident set size: 3652 pages
% 0.75/0.51
% 0.75/0.51 % -------------------------------------------------
% 0.75/0.51 % User time : 0.462 s
% 0.75/0.51 % System time : 0.045 s
% 0.75/0.51 % Total time : 0.507 s
% 0.75/0.51 % Maximum resident set size: 4608 pages
% 0.75/0.51 % E exiting
%------------------------------------------------------------------------------