TSTP Solution File: SWW829_1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWW829_1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 : Mon Jun 24 18:18:45 EDT 2024
% Result : Unsatisfiable 11.94s 2.13s
% Output : CNFRefutation 11.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW829_1 : TPTP v8.2.0. Released v7.0.0.
% 0.11/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 05:34:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.46 Running TFA theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.94/2.13 % SZS status Started for theBenchmark.p
% 11.94/2.13 % SZS status Unsatisfiable for theBenchmark.p
% 11.94/2.13
% 11.94/2.13 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 11.94/2.13
% 11.94/2.13 ------ iProver source info
% 11.94/2.13
% 11.94/2.13 git: date: 2024-06-12 09:56:46 +0000
% 11.94/2.13 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 11.94/2.13 git: non_committed_changes: false
% 11.94/2.13
% 11.94/2.13 ------ Parsing...
% 11.94/2.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 11.94/2.13
% 11.94/2.13 ------ Preprocessing... sup_sim: 147 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 11.94/2.13
% 11.94/2.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 11.94/2.13
% 11.94/2.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 11.94/2.13 ------ Proving...
% 11.94/2.13 ------ Problem Properties
% 11.94/2.13
% 11.94/2.13
% 11.94/2.13 clauses 367
% 11.94/2.13 conjectures 0
% 11.94/2.13 EPR 16
% 11.94/2.13 Horn 307
% 11.94/2.13 unary 255
% 11.94/2.13 binary 63
% 11.94/2.13 lits 559
% 11.94/2.13 lits eq 379
% 11.94/2.13 fd_pure 0
% 11.94/2.13 fd_pseudo 0
% 11.94/2.13 fd_cond 16
% 11.94/2.13 fd_pseudo_cond 10
% 11.94/2.13 AC symbols 4
% 11.94/2.13
% 11.94/2.13 ------ Input Options Time Limit: Unbounded
% 11.94/2.13
% 11.94/2.13
% 11.94/2.13 ------
% 11.94/2.13 Current options:
% 11.94/2.13 ------
% 11.94/2.13
% 11.94/2.13
% 11.94/2.13
% 11.94/2.13
% 11.94/2.13 ------ Proving...
% 11.94/2.13
% 11.94/2.13
% 11.94/2.13 % SZS status Unsatisfiable for theBenchmark.p
% 11.94/2.13
% 11.94/2.13 % SZS output start CNFRefutation for theBenchmark.p
% 11.94/2.13
% 11.94/2.13 tff(f2,axiom,(
% 11.94/2.13 ! [X0 : 'S2'] : ? [X1 : 'S3',X2 : $int] : (f3(f4,X0) = f5(f6(f7,f5(f6(f7,f3(X1,f16)),f3(X1,f11(f12,f17(f18(f19,f13(f14,f16)),X2))))),f3(f20,f11(f12,$sum(X2,1)))) & $product(2,f13(f14,X0)) = X2 & f8(f9,f3(f10,f11(f12,$product(2,f13(f14,f15))))) = X1)),
% 11.94/2.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_2)).
% 11.94/2.13
% 11.94/2.13 tff(f6,axiom,(
% 11.94/2.13 ! [X0 : 'S2'] : f3(f24,X0) = f5(f6(f7,f3(f8(f9,f3(f10,f11(f12,$product(2,f13(f14,f15))))),f16)),f5(f6(f7,f3(f8(f9,f3(f8(f9,f3(f10,f15)),f16)),X0)),f3(f20,f11(f12,$sum($product(2,f13(f14,X0)),1)))))),
% 11.94/2.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_6)).
% 11.94/2.13
% 11.94/2.13 tff(f9,axiom,(
% 11.94/2.13 ! [X0 : 'S3',X5 : 'S2'] : f3(f34(f35,X0),X5) = f3(X0,f11(f12,$sum($product(2,f13(f14,X5)),1)))),
% 11.94/2.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_9)).
% 11.94/2.13
% 11.94/2.13 tff(f13,axiom,(
% 11.94/2.13 ! [X0 : 'S3',X5 : 'S2'] : f3(f34(f42,X0),X5) = f3(X0,f11(f12,$product(2,f13(f14,X5))))),
% 11.94/2.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_13)).
% 11.94/2.13
% 11.94/2.13 tff(f30,axiom,(
% 11.94/2.13 ! [X0 : 'S9',X5 : $int,X6 : 'S2'] : f13(f72(f73(f74,X0),X5),X6) = f17(f18(f19,f13(X0,X6)),X5)),
% 11.94/2.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_30)).
% 11.94/2.13
% 11.94/2.13 tff(f64,axiom,(
% 11.94/2.13 ? [X25 : 'S34'] : (f78(f79(f80,f4),X25) != f78(f79(f80,f24),X25) & f81(f82(f11(f12,0)),f15) = X25)),
% 11.94/2.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_64)).
% 11.94/2.13
% 11.94/2.13 tff(f67,axiom,(
% 11.94/2.13 ! [X0 : 'S2',X5 : 'S2',X6 : 'S2'] : ? [X26 : 'S10',X27 : $int] : (f3(f8(f9,f3(f10,f11(f12,$product(2,f13(f14,X0))))),f11(f12,f17(X26,$product(2,X27)))) = f3(f8(f9,f3(f10,X0)),f11(f12,f17(X26,X27))) & f13(f14,X6) = X27 & f18(f19,f13(f14,X5)) = X26)),
% 11.94/2.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_67)).
% 11.94/2.13
% 11.94/2.13 tff(f204,axiom,(
% 11.94/2.13 ! [X0 : 'S4',X5 : 'S4',X6 : 'S4'] : ? [X167 : 'S5'] : (f5(f6(f7,f5(X167,X5)),X6) = f5(X167,f5(f6(f7,X5),X6)) & f6(f7,X0) = X167)),
% 11.94/2.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_204)).
% 11.94/2.13
% 11.94/2.13 tff(f216,axiom,(
% 11.94/2.13 ! [X0 : 'S4',X5 : 'S4'] : f5(f6(f7,X0),X5) = f5(f6(f7,X5),X0)),
% 11.94/2.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_216)).
% 11.94/2.13
% 11.94/2.13 tff(f274,axiom,(
% 11.94/2.13 ! [X0 : 'S4',X5 : 'S2',X6 : 'S2'] : ? [X232 : 'S3'] : (f3(f8(f9,f3(X232,X5)),X6) = f3(X232,f11(f12,f17(f18(f19,f13(f14,X5)),f13(f14,X6)))) & f8(f9,X0) = X232)),
% 11.94/2.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_274)).
% 11.94/2.13
% 11.94/2.13 tff(f366,axiom,(
% 11.94/2.13 ! [X0 : 'S34',X5 : 'S3',X6 : 'S3'] : (! [X15 : 'S2'] : (f1 = f148(X15,X0) => f3(X5,X15) = f3(X6,X15)) => f78(f79(f80,X5),X0) = f78(f79(f80,X6),X0))),
% 11.94/2.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_366)).
% 11.94/2.13
% 11.94/2.13 tff(f441,plain,(
% 11.94/2.13 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 11.94/2.13 introduced(theory_axiom_138,[])).
% 11.94/2.13
% 11.94/2.13 tff(f442,plain,(
% 11.94/2.13 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 11.94/2.13 introduced(theory_axiom_139,[])).
% 11.94/2.13
% 11.94/2.13 tff(f452,plain,(
% 11.94/2.13 ( ! [X0 : $int,X1 : $int] : ($product(X0,X1) = $product(X1,X0)) )),
% 11.94/2.13 introduced(theory_axiom_138,[])).
% 11.94/2.13
% 11.94/2.13 tff(f453,plain,(
% 11.94/2.13 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$product(X1,X2)) = $product($product(X0,X1),X2)) )),
% 11.94/2.13 introduced(theory_axiom_139,[])).
% 11.94/2.13
% 11.94/2.13 tff(f459,plain,(
% 11.94/2.13 ( ! [X0 : $real,X1 : $real] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 11.94/2.13 introduced(theory_axiom_138,[])).
% 11.94/2.13
% 11.94/2.13 tff(f460,plain,(
% 11.94/2.13 ( ! [X2 : $real,X0 : $real,X1 : $real] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 11.94/2.13 introduced(theory_axiom_139,[])).
% 11.94/2.13
% 11.94/2.13 tff(f470,plain,(
% 11.94/2.13 ( ! [X0 : $real,X1 : $real] : ($product(X0,X1) = $product(X1,X0)) )),
% 11.94/2.13 introduced(theory_axiom_138,[])).
% 11.94/2.13
% 11.94/2.13 tff(f471,plain,(
% 11.94/2.13 ( ! [X2 : $real,X0 : $real,X1 : $real] : ($product(X0,$product(X1,X2)) = $product($product(X0,X1),X2)) )),
% 11.94/2.13 introduced(theory_axiom_139,[])).
% 11.94/2.13
% 11.94/2.13 tff(f481,plain,(
% 11.94/2.13 ! [X0 : 'S3',X1 : 'S2'] : f3(f34(f35,X0),X1) = f3(X0,f11(f12,$sum($product(2,f13(f14,X1)),1)))),
% 11.94/2.13 inference(rectify,[],[f9])).
% 11.94/2.13
% 11.94/2.13 tff(f485,plain,(
% 11.94/2.13 ! [X0 : 'S3',X1 : 'S2'] : f3(f34(f42,X0),X1) = f3(X0,f11(f12,$product(2,f13(f14,X1))))),
% 11.94/2.13 inference(rectify,[],[f13])).
% 11.94/2.13
% 11.94/2.13 tff(f502,plain,(
% 11.94/2.13 ! [X0 : 'S9',X1 : $int,X2 : 'S2'] : f13(f72(f73(f74,X0),X1),X2) = f17(f18(f19,f13(X0,X2)),X1)),
% 11.94/2.13 inference(rectify,[],[f30])).
% 11.94/2.13
% 11.94/2.13 tff(f536,plain,(
% 11.94/2.13 ? [X0 : 'S34'] : (f78(f79(f80,f4),X0) != f78(f79(f80,f24),X0) & f81(f82(f11(f12,0)),f15) = X0)),
% 11.94/2.13 inference(rectify,[],[f64])).
% 11.94/2.13
% 11.94/2.13 tff(f537,plain,(
% 11.94/2.13 ! [X0 : 'S2',X1 : 'S2',X2 : 'S2'] : ? [X3 : 'S10',X4 : $int] : (f3(f8(f9,f3(f10,f11(f12,$product(2,f13(f14,X0))))),f11(f12,f17(X3,$product(2,X4)))) = f3(f8(f9,f3(f10,X0)),f11(f12,f17(X3,X4))) & f13(f14,X2) = X4 & f18(f19,f13(f14,X1)) = X3)),
% 11.94/2.13 inference(rectify,[],[f67])).
% 11.94/2.13
% 11.94/2.13 tff(f673,plain,(
% 11.94/2.13 ! [X0 : 'S4',X1 : 'S4',X2 : 'S4'] : ? [X3 : 'S5'] : (f5(f6(f7,f5(X3,X1)),X2) = f5(X3,f5(f6(f7,X1),X2)) & f6(f7,X0) = X3)),
% 11.94/2.13 inference(rectify,[],[f204])).
% 11.94/2.13
% 11.94/2.13 tff(f685,plain,(
% 11.94/2.13 ! [X0 : 'S4',X1 : 'S4'] : f5(f6(f7,X0),X1) = f5(f6(f7,X1),X0)),
% 11.94/2.13 inference(rectify,[],[f216])).
% 11.94/2.13
% 11.94/2.13 tff(f727,plain,(
% 11.94/2.13 ! [X0 : 'S4',X1 : 'S2',X2 : 'S2'] : ? [X3 : 'S3'] : (f3(f8(f9,f3(X3,X1)),X2) = f3(X3,f11(f12,f17(f18(f19,f13(f14,X1)),f13(f14,X2)))) & f8(f9,X0) = X3)),
% 11.94/2.13 inference(rectify,[],[f274])).
% 11.94/2.13
% 11.94/2.13 tff(f814,plain,(
% 11.94/2.13 ! [X0 : 'S34',X1 : 'S3',X2 : 'S3'] : (! [X3 : 'S2'] : (f1 = f148(X3,X0) => f3(X1,X3) = f3(X2,X3)) => f78(f79(f80,X1),X0) = f78(f79(f80,X2),X0))),
% 11.94/2.13 inference(rectify,[],[f366])).
% 11.94/2.13
% 11.94/2.13 tff(f886,plain,(
% 11.94/2.13 ! [X0 : 'S34',X1 : 'S3',X2 : 'S3'] : (f78(f79(f80,X1),X0) = f78(f79(f80,X2),X0) | ? [X3 : 'S2'] : (f3(X1,X3) != f3(X2,X3) & f1 = f148(X3,X0)))),
% 11.94/2.13 inference(ennf_transformation,[],[f814])).
% 11.94/2.13
% 11.94/2.13 tff(f927,plain,(
% 11.94/2.13 ! [X0 : 'S2'] : (? [X1 : 'S3',X2 : $int] : (f3(f4,X0) = f5(f6(f7,f5(f6(f7,f3(X1,f16)),f3(X1,f11(f12,f17(f18(f19,f13(f14,f16)),X2))))),f3(f20,f11(f12,$sum(X2,1)))) & $product(2,f13(f14,X0)) = X2 & f8(f9,f3(f10,f11(f12,$product(2,f13(f14,f15))))) = X1) => (f3(f4,X0) = f5(f6(f7,f5(f6(f7,f3(sK5(X0),f16)),f3(sK5(X0),f11(f12,f17(f18(f19,f13(f14,f16)),sK6(X0)))))),f3(f20,f11(f12,$sum(sK6(X0),1)))) & $product(2,f13(f14,X0)) = sK6(X0) & f8(f9,f3(f10,f11(f12,$product(2,f13(f14,f15))))) = sK5(X0)))),
% 11.94/2.14 introduced(choice_axiom,[])).
% 11.94/2.14
% 11.94/2.14 tff(f928,plain,(
% 11.94/2.14 ! [X0 : 'S2'] : (f3(f4,X0) = f5(f6(f7,f5(f6(f7,f3(sK5(X0),f16)),f3(sK5(X0),f11(f12,f17(f18(f19,f13(f14,f16)),sK6(X0)))))),f3(f20,f11(f12,$sum(sK6(X0),1)))) & $product(2,f13(f14,X0)) = sK6(X0) & f8(f9,f3(f10,f11(f12,$product(2,f13(f14,f15))))) = sK5(X0))),
% 11.94/2.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f2,f927])).
% 11.94/2.14
% 11.94/2.14 tff(f957,plain,(
% 11.94/2.14 ? [X0 : 'S34'] : (f78(f79(f80,f4),X0) != f78(f79(f80,f24),X0) & f81(f82(f11(f12,0)),f15) = X0) => (f78(f79(f80,f4),sK26) != f78(f79(f80,f24),sK26) & f81(f82(f11(f12,0)),f15) = sK26)),
% 11.94/2.14 introduced(choice_axiom,[])).
% 11.94/2.14
% 11.94/2.14 tff(f958,plain,(
% 11.94/2.14 f78(f79(f80,f4),sK26) != f78(f79(f80,f24),sK26) & f81(f82(f11(f12,0)),f15) = sK26),
% 11.94/2.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f536,f957])).
% 11.94/2.14
% 11.94/2.14 tff(f959,plain,(
% 11.94/2.14 ! [X0 : 'S2',X1 : 'S2',X2 : 'S2'] : (? [X3 : 'S10',X4 : $int] : (f3(f8(f9,f3(f10,f11(f12,$product(2,f13(f14,X0))))),f11(f12,f17(X3,$product(2,X4)))) = f3(f8(f9,f3(f10,X0)),f11(f12,f17(X3,X4))) & f13(f14,X2) = X4 & f18(f19,f13(f14,X1)) = X3) => (f3(f8(f9,f3(f10,f11(f12,$product(2,f13(f14,X0))))),f11(f12,f17(sK27(X0,X1,X2),$product(2,sK28(X0,X1,X2))))) = f3(f8(f9,f3(f10,X0)),f11(f12,f17(sK27(X0,X1,X2),sK28(X0,X1,X2)))) & f13(f14,X2) = sK28(X0,X1,X2) & f18(f19,f13(f14,X1)) = sK27(X0,X1,X2)))),
% 11.94/2.14 introduced(choice_axiom,[])).
% 11.94/2.14
% 11.94/2.14 tff(f960,plain,(
% 11.94/2.14 ! [X0 : 'S2',X1 : 'S2',X2 : 'S2'] : (f3(f8(f9,f3(f10,f11(f12,$product(2,f13(f14,X0))))),f11(f12,f17(sK27(X0,X1,X2),$product(2,sK28(X0,X1,X2))))) = f3(f8(f9,f3(f10,X0)),f11(f12,f17(sK27(X0,X1,X2),sK28(X0,X1,X2)))) & f13(f14,X2) = sK28(X0,X1,X2) & f18(f19,f13(f14,X1)) = sK27(X0,X1,X2))),
% 11.94/2.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f537,f959])).
% 11.94/2.14
% 11.94/2.14 tff(f1173,plain,(
% 11.94/2.14 ! [X0 : 'S4',X1 : 'S4',X2 : 'S4'] : (? [X3 : 'S5'] : (f5(f6(f7,f5(X3,X1)),X2) = f5(X3,f5(f6(f7,X1),X2)) & f6(f7,X0) = X3) => (f5(f6(f7,f5(sK168(X0,X1,X2),X1)),X2) = f5(sK168(X0,X1,X2),f5(f6(f7,X1),X2)) & f6(f7,X0) = sK168(X0,X1,X2)))),
% 11.94/2.14 introduced(choice_axiom,[])).
% 11.94/2.14
% 11.94/2.14 tff(f1174,plain,(
% 11.94/2.14 ! [X0 : 'S4',X1 : 'S4',X2 : 'S4'] : (f5(f6(f7,f5(sK168(X0,X1,X2),X1)),X2) = f5(sK168(X0,X1,X2),f5(f6(f7,X1),X2)) & f6(f7,X0) = sK168(X0,X1,X2))),
% 11.94/2.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK168])],[f673,f1173])).
% 11.94/2.14
% 11.94/2.14 tff(f1269,plain,(
% 11.94/2.14 ! [X0 : 'S4',X1 : 'S2',X2 : 'S2'] : (? [X3 : 'S3'] : (f3(f8(f9,f3(X3,X1)),X2) = f3(X3,f11(f12,f17(f18(f19,f13(f14,X1)),f13(f14,X2)))) & f8(f9,X0) = X3) => (f3(f8(f9,f3(sK233(X0,X1,X2),X1)),X2) = f3(sK233(X0,X1,X2),f11(f12,f17(f18(f19,f13(f14,X1)),f13(f14,X2)))) & f8(f9,X0) = sK233(X0,X1,X2)))),
% 11.94/2.14 introduced(choice_axiom,[])).
% 11.94/2.14
% 11.94/2.14 tff(f1270,plain,(
% 11.94/2.14 ! [X0 : 'S4',X1 : 'S2',X2 : 'S2'] : (f3(f8(f9,f3(sK233(X0,X1,X2),X1)),X2) = f3(sK233(X0,X1,X2),f11(f12,f17(f18(f19,f13(f14,X1)),f13(f14,X2)))) & f8(f9,X0) = sK233(X0,X1,X2))),
% 11.94/2.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK233])],[f727,f1269])).
% 11.94/2.14
% 11.94/2.14 tff(f1421,plain,(
% 11.94/2.14 ! [X0 : 'S34',X1 : 'S3',X2 : 'S3'] : (? [X3 : 'S2'] : (f3(X1,X3) != f3(X2,X3) & f1 = f148(X3,X0)) => (f3(X1,sK306(X0,X1,X2)) != f3(X2,sK306(X0,X1,X2)) & f1 = f148(sK306(X0,X1,X2),X0)))),
% 11.94/2.14 introduced(choice_axiom,[])).
% 11.94/2.14
% 11.94/2.14 tff(f1422,plain,(
% 11.94/2.14 ! [X0 : 'S34',X1 : 'S3',X2 : 'S3'] : (f78(f79(f80,X1),X0) = f78(f79(f80,X2),X0) | (f3(X1,sK306(X0,X1,X2)) != f3(X2,sK306(X0,X1,X2)) & f1 = f148(sK306(X0,X1,X2),X0)))),
% 11.94/2.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK306])],[f886,f1421])).
% 11.94/2.14
% 11.94/2.14 tff(f1446,plain,(
% 11.94/2.14 ( ! [X0 : 'S2'] : (f8(f9,f3(f10,f11(f12,$product(2,f13(f14,f15))))) = sK5(X0)) )),
% 11.94/2.14 inference(cnf_transformation,[],[f928])).
% 11.94/2.14
% 11.94/2.14 tff(f1447,plain,(
% 11.94/2.14 ( ! [X0 : 'S2'] : ($product(2,f13(f14,X0)) = sK6(X0)) )),
% 11.94/2.14 inference(cnf_transformation,[],[f928])).
% 11.94/2.14
% 11.94/2.14 tff(f1448,plain,(
% 11.94/2.14 ( ! [X0 : 'S2'] : (f3(f4,X0) = f5(f6(f7,f5(f6(f7,f3(sK5(X0),f16)),f3(sK5(X0),f11(f12,f17(f18(f19,f13(f14,f16)),sK6(X0)))))),f3(f20,f11(f12,$sum(sK6(X0),1))))) )),
% 11.94/2.14 inference(cnf_transformation,[],[f928])).
% 11.94/2.14
% 11.94/2.14 tff(f1454,plain,(
% 11.94/2.14 ( ! [X0 : 'S2'] : (f3(f24,X0) = f5(f6(f7,f3(f8(f9,f3(f10,f11(f12,$product(2,f13(f14,f15))))),f16)),f5(f6(f7,f3(f8(f9,f3(f8(f9,f3(f10,f15)),f16)),X0)),f3(f20,f11(f12,$sum($product(2,f13(f14,X0)),1)))))) )),
% 11.94/2.14 inference(cnf_transformation,[],[f6])).
% 11.94/2.14
% 11.94/2.14 tff(f1457,plain,(
% 11.94/2.14 ( ! [X0 : 'S3',X1 : 'S2'] : (f3(f34(f35,X0),X1) = f3(X0,f11(f12,$sum($product(2,f13(f14,X1)),1)))) )),
% 11.94/2.14 inference(cnf_transformation,[],[f481])).
% 11.94/2.14
% 11.94/2.14 tff(f1461,plain,(
% 11.94/2.14 ( ! [X0 : 'S3',X1 : 'S2'] : (f3(f34(f42,X0),X1) = f3(X0,f11(f12,$product(2,f13(f14,X1))))) )),
% 11.94/2.14 inference(cnf_transformation,[],[f485])).
% 11.94/2.14
% 11.94/2.14 tff(f1478,plain,(
% 11.94/2.14 ( ! [X2 : 'S2',X0 : 'S9',X1 : $int] : (f13(f72(f73(f74,X0),X1),X2) = f17(f18(f19,f13(X0,X2)),X1)) )),
% 11.94/2.14 inference(cnf_transformation,[],[f502])).
% 11.94/2.14
% 11.94/2.14 tff(f1530,plain,(
% 11.94/2.14 f78(f79(f80,f4),sK26) != f78(f79(f80,f24),sK26)),
% 11.94/2.14 inference(cnf_transformation,[],[f958])).
% 11.94/2.14
% 11.94/2.14 tff(f1533,plain,(
% 11.94/2.14 ( ! [X2 : 'S2',X0 : 'S2',X1 : 'S2'] : (f18(f19,f13(f14,X1)) = sK27(X0,X1,X2)) )),
% 11.94/2.14 inference(cnf_transformation,[],[f960])).
% 11.94/2.14
% 11.94/2.14 tff(f1534,plain,(
% 11.94/2.14 ( ! [X2 : 'S2',X0 : 'S2',X1 : 'S2'] : (f13(f14,X2) = sK28(X0,X1,X2)) )),
% 11.94/2.14 inference(cnf_transformation,[],[f960])).
% 11.94/2.14
% 11.94/2.14 tff(f1535,plain,(
% 11.94/2.14 ( ! [X2 : 'S2',X0 : 'S2',X1 : 'S2'] : (f3(f8(f9,f3(f10,f11(f12,$product(2,f13(f14,X0))))),f11(f12,f17(sK27(X0,X1,X2),$product(2,sK28(X0,X1,X2))))) = f3(f8(f9,f3(f10,X0)),f11(f12,f17(sK27(X0,X1,X2),sK28(X0,X1,X2))))) )),
% 11.94/2.14 inference(cnf_transformation,[],[f960])).
% 11.94/2.14
% 11.94/2.14 tff(f1828,plain,(
% 11.94/2.14 ( ! [X2 : 'S4',X0 : 'S4',X1 : 'S4'] : (f6(f7,X0) = sK168(X0,X1,X2)) )),
% 11.94/2.14 inference(cnf_transformation,[],[f1174])).
% 11.94/2.14
% 11.94/2.14 tff(f1829,plain,(
% 11.94/2.14 ( ! [X2 : 'S4',X0 : 'S4',X1 : 'S4'] : (f5(f6(f7,f5(sK168(X0,X1,X2),X1)),X2) = f5(sK168(X0,X1,X2),f5(f6(f7,X1),X2))) )),
% 11.94/2.14 inference(cnf_transformation,[],[f1174])).
% 11.94/2.14
% 11.94/2.14 tff(f1854,plain,(
% 11.94/2.14 ( ! [X0 : 'S4',X1 : 'S4'] : (f5(f6(f7,X0),X1) = f5(f6(f7,X1),X0)) )),
% 11.94/2.14 inference(cnf_transformation,[],[f685])).
% 11.94/2.14
% 11.94/2.14 tff(f1964,plain,(
% 11.94/2.14 ( ! [X2 : 'S2',X0 : 'S4',X1 : 'S2'] : (f8(f9,X0) = sK233(X0,X1,X2)) )),
% 11.94/2.14 inference(cnf_transformation,[],[f1270])).
% 11.94/2.14
% 11.94/2.14 tff(f1965,plain,(
% 11.94/2.14 ( ! [X2 : 'S2',X0 : 'S4',X1 : 'S2'] : (f3(f8(f9,f3(sK233(X0,X1,X2),X1)),X2) = f3(sK233(X0,X1,X2),f11(f12,f17(f18(f19,f13(f14,X1)),f13(f14,X2))))) )),
% 11.94/2.14 inference(cnf_transformation,[],[f1270])).
% 11.94/2.14
% 11.94/2.14 tff(f2168,plain,(
% 11.94/2.14 ( ! [X2 : 'S3',X0 : 'S34',X1 : 'S3'] : (f78(f79(f80,X1),X0) = f78(f79(f80,X2),X0) | f3(X1,sK306(X0,X1,X2)) != f3(X2,sK306(X0,X1,X2))) )),
% 11.94/2.14 inference(cnf_transformation,[],[f1422])).
% 11.94/2.14
% 11.94/2.14 tff(f2228,plain,(
% 11.94/2.14 ( ! [X0 : 'S2'] : (f3(f4,X0) = f5(f6(f7,f5(f6(f7,f3(f8(f9,f3(f10,f11(f12,$product(2,f13(f14,f15))))),f16)),f3(f8(f9,f3(f10,f11(f12,$product(2,f13(f14,f15))))),f11(f12,f17(f18(f19,f13(f14,f16)),$product(2,f13(f14,X0))))))),f3(f20,f11(f12,$sum($product(2,f13(f14,X0)),1))))) )),
% 11.94/2.14 inference(definition_unfolding,[],[f1448,f1446,f1446,f1447,f1447])).
% 11.94/2.14
% 11.94/2.14 tff(f2241,plain,(
% 11.94/2.14 ( ! [X2 : 'S2',X0 : 'S2',X1 : 'S2'] : (f3(f8(f9,f3(f10,f11(f12,$product(2,f13(f14,X0))))),f11(f12,f17(f18(f19,f13(f14,X1)),$product(2,f13(f14,X2))))) = f3(f8(f9,f3(f10,X0)),f11(f12,f17(f18(f19,f13(f14,X1)),f13(f14,X2))))) )),
% 11.94/2.14 inference(definition_unfolding,[],[f1535,f1533,f1534,f1533,f1534])).
% 11.94/2.14
% 11.94/2.14 tff(f2351,plain,(
% 11.94/2.14 ( ! [X2 : 'S4',X0 : 'S4',X1 : 'S4'] : (f5(f6(f7,f5(f6(f7,X0),X1)),X2) = f5(f6(f7,X0),f5(f6(f7,X1),X2))) )),
% 11.94/2.14 inference(definition_unfolding,[],[f1829,f1828,f1828])).
% 11.94/2.14
% 11.94/2.14 tff(f2398,plain,(
% 11.94/2.14 ( ! [X2 : 'S2',X0 : 'S4',X1 : 'S2'] : (f3(f8(f9,f3(f8(f9,X0),X1)),X2) = f3(f8(f9,X0),f11(f12,f17(f18(f19,f13(f14,X1)),f13(f14,X2))))) )),
% 11.94/2.14 inference(definition_unfolding,[],[f1965,f1964,f1964])).
% 11.94/2.14
% 11.94/2.14 cnf(c_53,plain,
% 11.94/2.14 ($product_real($product_real(X0_2,X1_2),X2_2) = $product_real(X0_2,$product_real(X1_2,X2_2))),
% 11.94/2.14 inference(cnf_transformation,[],[f471])).
% 11.94/2.14
% 11.94/2.14 cnf(c_54,plain,
% 11.94/2.14 ($product_real(X0_2,X1_2) = $product_real(X1_2,X0_2)),
% 11.94/2.14 inference(cnf_transformation,[],[f470])).
% 11.94/2.14
% 11.94/2.14 cnf(c_64,plain,
% 11.94/2.14 ($sum_real($sum_real(X0_2,X1_2),X2_2) = $sum_real(X0_2,$sum_real(X1_2,X2_2))),
% 11.94/2.14 inference(cnf_transformation,[],[f460])).
% 11.94/2.14
% 11.94/2.14 cnf(c_65,plain,
% 11.94/2.14 ($sum_real(X0_2,X1_2) = $sum_real(X1_2,X0_2)),
% 11.94/2.14 inference(cnf_transformation,[],[f459])).
% 11.94/2.14
% 11.94/2.14 cnf(c_71,plain,
% 11.94/2.14 ($product_int($product_int(X0_3,X1_3),X2_3) = $product_int(X0_3,$product_int(X1_3,X2_3))),
% 11.94/2.14 inference(cnf_transformation,[],[f453])).
% 11.94/2.14
% 11.94/2.14 cnf(c_72,plain,
% 11.94/2.14 ($product_int(X0_3,X1_3) = $product_int(X1_3,X0_3)),
% 11.94/2.14 inference(cnf_transformation,[],[f452])).
% 11.94/2.14
% 11.94/2.14 cnf(c_82,plain,
% 11.94/2.14 ($sum_int($sum_int(X0_3,X1_3),X2_3) = $sum_int(X0_3,$sum_int(X1_3,X2_3))),
% 11.94/2.14 inference(cnf_transformation,[],[f442])).
% 11.94/2.14
% 11.94/2.14 cnf(c_83,plain,
% 11.94/2.14 ($sum_int(X0_3,X1_3) = $sum_int(X1_3,X0_3)),
% 11.94/2.14 inference(cnf_transformation,[],[f441])).
% 11.94/2.14
% 11.94/2.14 cnf(c_85,plain,
% 11.94/2.14 (f5(f6(f7,f5(f6(f7,f3(f8(f9,f3(f10,f11(f12,$product_int(2,f13(f14,f15))))),f16)),f3(f8(f9,f3(f10,f11(f12,$product_int(2,f13(f14,f15))))),f11(f12,f17(f18(f19,f13(f14,f16)),$product_int(2,f13(f14,X0_13))))))),f3(f20,f11(f12,$sum_int($product_int(2,f13(f14,X0_13)),1)))) = f3(f4,X0_13)),
% 11.94/2.14 inference(cnf_transformation,[],[f2228])).
% 11.94/2.14
% 11.94/2.14 cnf(c_89,plain,
% 11.94/2.14 (f5(f6(f7,f3(f8(f9,f3(f10,f11(f12,$product_int(2,f13(f14,f15))))),f16)),f5(f6(f7,f3(f8(f9,f3(f8(f9,f3(f10,f15)),f16)),X0_13)),f3(f20,f11(f12,$sum_int($product_int(2,f13(f14,X0_13)),1))))) = f3(f24,X0_13)),
% 11.94/2.14 inference(cnf_transformation,[],[f1454])).
% 11.94/2.14
% 11.94/2.14 cnf(c_92,plain,
% 11.94/2.14 (f3(X0_36,f11(f12,$sum_int($product_int(2,f13(f14,X0_13)),1))) = f3(f34(f35,X0_36),X0_13)),
% 11.94/2.14 inference(cnf_transformation,[],[f1457])).
% 11.94/2.14
% 11.94/2.14 cnf(c_96,plain,
% 11.94/2.14 (f3(X0_36,f11(f12,$product_int(2,f13(f14,X0_13)))) = f3(f34(f42,X0_36),X0_13)),
% 11.94/2.14 inference(cnf_transformation,[],[f1461])).
% 11.94/2.14
% 11.94/2.14 cnf(c_113,plain,
% 11.94/2.14 (f13(f72(f73(f74,X0_17),X0_3),X0_13) = f17(f18(f19,f13(X0_17,X0_13)),X0_3)),
% 11.94/2.14 inference(cnf_transformation,[],[f1478])).
% 11.94/2.14
% 11.94/2.14 cnf(c_147,plain,
% 11.94/2.14 (f78(f79(f80,f4),sK26) != f78(f79(f80,f24),sK26)),
% 11.94/2.14 inference(cnf_transformation,[],[f1530])).
% 11.94/2.14
% 11.94/2.14 cnf(c_151,plain,
% 11.94/2.14 (f3(f8(f9,f3(f10,f11(f12,$product_int(2,f13(f14,X0_13))))),f11(f12,f17(f18(f19,f13(f14,X1_13)),$product_int(2,f13(f14,X2_13))))) = f3(f8(f9,f3(f10,X0_13)),f11(f12,f17(f18(f19,f13(f14,X1_13)),f13(f14,X2_13))))),
% 11.94/2.14 inference(cnf_transformation,[],[f2241])).
% 11.94/2.14
% 11.94/2.14 cnf(c_299,plain,
% 11.94/2.14 (f5(f6(f7,f5(f6(f7,X0_24),X1_24)),X2_24) = f5(f6(f7,X0_24),f5(f6(f7,X1_24),X2_24))),
% 11.94/2.14 inference(cnf_transformation,[],[f2351])).
% 11.94/2.14
% 11.94/2.14 cnf(c_311,plain,
% 11.94/2.14 (f5(f6(f7,X0_24),X1_24) = f5(f6(f7,X1_24),X0_24)),
% 11.94/2.14 inference(cnf_transformation,[],[f1854])).
% 11.94/2.14
% 11.94/2.14 cnf(c_370,plain,
% 11.94/2.14 (f3(f8(f9,X0_24),f11(f12,f17(f18(f19,f13(f14,X0_13)),f13(f14,X1_13)))) = f3(f8(f9,f3(f8(f9,X0_24),X0_13)),X1_13)),
% 11.94/2.14 inference(cnf_transformation,[],[f2398])).
% 11.94/2.14
% 11.94/2.14 cnf(c_504,plain,
% 11.94/2.14 (f3(X0_36,sK306(X0_62,X0_36,X1_36)) != f3(X1_36,sK306(X0_62,X0_36,X1_36))|
% 11.94/2.14 f78(f79(f80,X0_36),X0_62) = f78(f79(f80,X1_36),X0_62)),
% 11.94/2.14 inference(cnf_transformation,[],[f2168])).
% 11.94/2.14
% 11.94/2.14 cnf(c_909,plain,
% 11.94/2.14 (f5(f6(f7,f5(f6(f7,f3(f8(f9,f3(f10,f11(f12,$product_int(2,f13(f14,f15))))),f16)),f3(f8(f9,f3(f10,f11(f12,$product_int(2,f13(f14,f15))))),f11(f12,f17(f18(f19,f13(f14,f16)),$product_int(2,f13(f14,X0_13))))))),f3(f20,f11(f12,$sum_int(1,$product_int(2,f13(f14,X0_13)))))) = f3(f4,X0_13)),
% 11.94/2.14 inference(theory_normalisation,
% 11.94/2.14 [status(thm)],
% 11.94/2.14 [c_85,c_71,c_72,c_82,c_83,c_53,c_54,c_64,c_65])).
% 11.94/2.14
% 11.94/2.14 cnf(c_911,plain,
% 11.94/2.14 (f5(f6(f7,f3(f8(f9,f3(f10,f11(f12,$product_int(2,f13(f14,f15))))),f16)),f5(f6(f7,f3(f8(f9,f3(f8(f9,f3(f10,f15)),f16)),X0_13)),f3(f20,f11(f12,$sum_int(1,$product_int(2,f13(f14,X0_13))))))) = f3(f24,X0_13)),
% 11.94/2.14 inference(theory_normalisation,
% 11.94/2.14 [status(thm)],
% 11.94/2.14 [c_89,c_71,c_72,c_82,c_83,c_53,c_54,c_64,c_65])).
% 11.94/2.14
% 11.94/2.14 cnf(c_913,plain,
% 11.94/2.14 (f3(X0_36,f11(f12,$sum_int(1,$product_int(2,f13(f14,X0_13))))) = f3(f34(f35,X0_36),X0_13)),
% 11.94/2.14 inference(theory_normalisation,
% 11.94/2.14 [status(thm)],
% 11.94/2.14 [c_92,c_71,c_72,c_82,c_83,c_53,c_54,c_64,c_65])).
% 11.94/2.14
% 11.94/2.14 cnf(c_3326,plain,
% 11.94/2.14 (f3(f8(f9,X0_24),f11(f12,f13(f72(f73(f74,f14),f13(f14,X0_13)),X1_13))) = f3(f8(f9,f3(f8(f9,X0_24),X1_13)),X0_13)),
% 11.94/2.14 inference(demodulation,[status(thm)],[c_370,c_113])).
% 11.94/2.14
% 11.94/2.14 cnf(c_3623,plain,
% 11.94/2.14 (f3(f8(f9,f3(f34(f42,f10),X0_13)),f11(f12,f13(f72(f73(f74,f14),$product_int(2,f13(f14,X1_13))),X2_13))) = f3(f8(f9,f3(f8(f9,f3(f10,X0_13)),X2_13)),X1_13)),
% 11.94/2.14 inference(demodulation,[status(thm)],[c_151,c_96,c_113,c_3326])).
% 11.94/2.14
% 11.94/2.14 cnf(c_3638,plain,
% 11.94/2.14 (f5(f6(f7,f3(f8(f9,f3(f34(f42,f10),f15)),f16)),f5(f6(f7,f3(f34(f35,f20),X0_13)),f3(f8(f9,f3(f8(f9,f3(f10,f15)),f16)),X0_13))) = f3(f24,X0_13)),
% 11.94/2.14 inference(demodulation,[status(thm)],[c_911,c_96,c_311,c_913])).
% 11.94/2.14
% 11.94/2.14 cnf(c_3650,plain,
% 11.94/2.14 (f3(f4,X0_13) = f3(f24,X0_13)),
% 11.94/2.14 inference(demodulation,
% 11.94/2.14 [status(thm)],
% 11.94/2.14 [c_909,c_96,c_113,c_299,c_311,c_913,c_3623,c_3638])).
% 11.94/2.14
% 11.94/2.14 cnf(c_16867,plain,
% 11.94/2.14 (f3(f4,sK306(sK26,f4,f24)) != f3(f24,sK306(sK26,f4,f24))|f78(f79(f80,f4),sK26) = f78(f79(f80,f24),sK26)),
% 11.94/2.14 inference(instantiation,[status(thm)],[c_504])).
% 11.94/2.14
% 11.94/2.14 cnf(c_17381,plain,
% 11.94/2.14 (f3(f4,sK306(sK26,f4,f24)) = f3(f24,sK306(sK26,f4,f24))),
% 11.94/2.14 inference(instantiation,[status(thm)],[c_3650])).
% 11.94/2.14
% 11.94/2.14 cnf(c_17382,plain,
% 11.94/2.14 ($false),
% 11.94/2.14 inference(prop_impl_just,[status(thm)],[c_17381,c_16867,c_147])).
% 11.94/2.14
% 11.94/2.14
% 11.94/2.14 % SZS output end CNFRefutation for theBenchmark.p
% 11.94/2.14
% 11.94/2.14
%------------------------------------------------------------------------------